The Count of Monte Cristo is a famous adventure novel by Alexandre Dumas. Hollywood filmed it many times; on stage, playwright Eugene O’Neill’s father, James O’Neill, made the role famous. The 1922 film version of Monte Cristo, starring actor John Gilbert, probably inspired the sandwich name.
 
It is not clear what dining establishment chose the sandwich name “Monte Cristo.” The sandwich name is cited in print from at least 1923, with the name possibly originating in Los Angeles. The Monte Cristo Hotel in Everett, Washington was constructed in 1925—although the sandwich was served at the hotel, there is no basis to assume that the sandwich originated there.
   
The Monte Cristo sandwich has roots and similarities to the grilled cheese sandwich and the ham sandwich, but is most nearly identified with the French sandwich Croque Monsieur. A 1924 recipe in the Los Angeles Times shows the Monte Cristo to be a cheese and ham sandwich, dipped in beaten egg and fried in hot butter.
 
 
Wikipedia: Monte Cristo sandwich
A Monte Cristo is a sandwich of ham, turkey, and Swiss cheese between batter-dipped grilled or fried bread.
 
The sandwich can differ regionally. Traditionally it is dipped in its entirety in batter and deep fried. In some regions of the United States it is served grilled, and in some regions it is served as an open sandwich with just the bread battered.
 
The sandwich is often served with fresh fruit or with clotted cream on the side. It is sometimes served with fruit preserves, powdered sugar, maple syrup, or sweet mustard sauce. The Cumberland Head-style Monte Cristo is served with Thousand Island dressing or Russian dressing.
 
Origins
According to food historian Linda Stradley, the Monte Cristo is a variation of the French croque-monsieur. In the 1930s–1960s, American cookbooks had recipes for this sandwich under such names as French Sandwich, Toasted Ham Sandwich, and French Toasted Cheese Sandwich. The first well documented appearance of the Monte Cristo sandwich is on the menu of the now-defunct Monte Cristo Hotel in Everett, Washington in the late 1920’s.
   
Wikipedia: The Count of Monte Cristo
The Count of Monte Cristo (French: Le Comte de Monte-Cristo) is an adventure novel by Alexandre Dumas, père. It is often considered to be, along with The Three Musketeers, Dumas’ most popular work. It is also among the highest selling books of all time. The writing of the work was completed in 1844. Like many of his novels, it is expanded from the plot outlines suggested by his collaborating ghostwriter Auguste Maquet.
 
The story takes place in France, Italy, islands in the Mediterranean and the Levant during the historical events of 1815–1838 (from just before the Hundred Days through to the reign of Louis-Philippe of France). The historical setting is a fundamental element of the book. It is primarily concerned with themes of hope, justice, vengeance, mercy, forgiveness and death, and is told in the style of an adventure story.
     
January 1923, The Caterer and Hotel Proprietors’ Gazette, pg. 32, col. 1:
Sandwiches
(...)
Monte Cristo… 50
 
24 May 1924, Los Angeles (CA) Daily Times, “Practical Recipes: Help for Epicures and All Who Appreciate Good Cooking” by Chef A. L. Wyman, pt. 1, pg. 6, col. 6:
MONTE CRISTO SANDWICH
Cover six slices of sandwich bread with a slice of American full cream cheese, cover the cheese with slices of boiled ham, cover with slices of bread, tie with white string, dip in beaten egg and fry a nice brown on both sides in hot butter. Place on hot plates, remove the string and serve.
 
3 September 1926, Fresno (CA) Bee, pg. 12, col. 3 ad:
Monte Cristo Sandwiches
(Greenlan—ed.)
     
9 August 1929, Los Angeles (CA) Times, “Practical Recipes,” pt. 2, pg. 7, col. 2:
MONTE CRISTO SANDWICH
Mrs. B, Los Angeles: Slice sandwich bread very thin and trim off the crusts, fit a slice of full cream cheese over the bread and over this place a slice of cold boiled ham, cover with a slice of bread and bind the sandwich together with a piece of string, beat the yolk of an egg with two tablespoonsful of water, dip the sandwich in this on both sides and fry slowly in hot butter until brown on both sides, remove the string and serve on a hot platter, garnish with slices of pickle.
   
11 August 1929, Indianapolis (IN) Sunday Star, “Diet to Add Weight Recommended” by Louella O. Parsons, pt. 7, pg. 2, col. 2:
I have personally watch Seena Owen devour Monte Cristo sandwiches, a delectable combination of ham, cheese and chicken fried in butter, and still not add an ounce to her weight.
 
June 1936, Restaurant Management, pp. 412-413:
Hy’s Three-Ring Circus MENU MAKING
E. A. Bachman, proprietor of the Annex, Portland, Oregon, features Hy Frager, the famous American chef who peps up menu listings with verbal acrobatics.
(Pg. 413, col. 1—ed.)
Combination Sandwiches
“CLUBHOUSE” (Breast of Chicken, Crisp Premium Bacon, Tomato, Lettuce, Pickles and Olives)... .40
“RUEBEN” (Not “Reuben”—ed.) (Baked Premium Ham, White Meat Chicken, Coquille Swiss Cheese and Tomato on Russian Rye)... .45
“MONTE CRISTO” (Baked Ham and Coquille Swiss Cheese, French Toasted in Butter)... .35
“ANNEX” (Oregon’s Choice Yaquina Oysters, Ham, Green Peppers in Butter, Cream and Eggs)... .45
(Col. 2—ed.)
“POP” (Chicken Salad, Lettuce, Tomato and Bacon, Olives)... .30
“HOLC” (Baked Ham, Peanut Butter and India Relish)... .25
“PWA” (Tuna Fish, Tomato, Lettuce and 1000 Isle)... .25
“FOREST SERVICE” (Baked Beans, Chili Sauce and Bacon)...  .25
“FRENCH DIP SANDWICH” (A crispy, crunchy Hard Roll w/ an amazing filling of Barbecued Meat, Swiss Cheese and a spicy, tangy Wine Sauce that combines into a superb bouquet of flavor)... .20
 
20 September 1936, Oakland (CA) Tribune, pg. 4S, col. 7 ad:
Chef Beyl will present three of his most popular recipes for the late-supper menus: “Lobster Thermidore,” “Monte Cristo Sandwich” and “Tomato Stuffed with Tuna.”
(Chef ‘Joe’ Beyl of the Athens Club—ed.)
 
28 July 1937, San Antonio (TX) Light, “Around the Plaza” by Jeff Davis, pg. 1, col. 1:
Mrs. Elliott Scott postcarding back from Hollywood that you haven’t lived until you’ve eaten one of the Monte Cristo sandwiches at the Brown Derby.
     
Google Books
Onions in the Stew
By Betty Bard MacDonald
Philadelphia, PA: Lippincott
1955
Pg. 181:
One of Don’s culinary specialties is Monte Cristo sandwiches, a concoction of ham, Swiss cheese, turkey between two slices of white bread, the whole dipped…
 
May 1955, Gourmet, pg. 66, col. 3:
Q. I’m giving a stag party, and want to serve Monte Cristo sandwiches.  I’ve looked everywhere, including my copy of THE GOURMET COOKBOOK, for the recipe, but no luck.
ROBERT H. MIDDOUGH
LONG BEACH, CALIFORNIA
A.  S’truth, the recipe was masquerading under the title of croque monsieur. Here’s an Americanized version of a famous French snack.
Monte Cristo Sandwich
Cut the crusts from 3 thin slices of white bread. Spread the first slice with butter and cover with lean baked ham and chicken. Butter the second slice on both sides, lay it on the ham and chicken and cover with thin slices of Swiss cheese. Finish with the third slice (Pg. 67, col. 1—ed.) of bread. Cut the sandwich in half, fasten the halves with wooden toothpicks, and dip them in a batter made of 2 eggs lightly beaten with 1 cup cold milk and seasoned to taste with salt and white pepper. Saute the sandwich in butter until golden brown on both sides.  Remove the picks and serve immediately.
   
12 November 1964, Los Angeles (CA) Times, “A Monte Cristo Sandwich That Counts,” food section, pg. D17:
A Monte Cristo Sandwich is an elegant concoction said to have originated in San Francisco, but now popular everywhere. It consists of sliced chicken or turkey and Swiss cheese sandwiched between…
   
July 1968, Gourmet, pg. 53, col. 2:
Q: My husband is Danish and trained in restaurant work, and we have just arrived in California from Copenhagen. We were recently served a Monte
Cristo sandwich at a Los Angeles restaurant, and are most interested in learning the recipe. We have been given a subscription to your magazine and are very pleased with the many fine features you have.
MRS. FLEMMING LINDBERG
LOS ANGELES, CALIFORNIA
A: Perhaps named after the Count, here is
Monte Cristo Sandwich
Butter a slice of white bread and cover it with sliced lean baked ham and sliced cooked chicken. Butter a second slice on both sides, place it on the meat, and cover it with thinly sliced Swiss cheese. Butter a third slice and place it, buttered side down, over the cheese. Trim away the crusts and cut the sandwich in half. Secure the halves with wooden picks, dip them in beaten egg, and saute them in butter on both sides until they are golden brown. Remove the picks and serve the sandwich with currant jelly, strawberry jam, or cranberry sauce. Serves 1.
 
Google News Archive
21 January 1970, Pittsburgh (PA) Post-Gazette, pg. 27?, col. 2:
Monte Cristo Sandwich
Basically this is a deep-fried sandwich which gets its tang from the combination of horseradish, mustard and cheese. The chef uses tongs to hold it while immersing it in the batter. He lets excess batter drip off before frying the sandwich. Hot German Potato Salad goes well with the Monte Cristo, he says.
18 slices white bread
12 (1 oz. slices of ham
12 (1 oz. slices of swiss cheese
1/4 cup mustard
1/4 cup horseradish
1 1/2 cups flour
1/2 teaspoon salt
1 tablespoon baking powder
4 eggs (well beaten)
3 cups milk (...)