A “Texas Dip” sandwich is a new variation on the “French Dip” sandwich that was invented in California. The Texas version consists of thinly sliced brisked, BBQ sauce, and Swiss cheese served on French bread.
 
     
Wikipedia: French Dip Sandwich
A French dip sandwich, also known as a beef dip, is a hot sandwich consisting of thinly sliced roast beef on a “French roll” or baguette. It is most commonly served au jus (“with juices”), that is, with a few ounces of beef juice collected during cooking. Broth can be substituted but that is frowned upon by connoisseurs. Cheese is optional.

Although the sandwich is most commonly served with a cup of jus or broth on the side of the plate, into which the sandwich is dipped as it is eaten, this is not how the sandwich was served when it was invented.
       
Big D’s Smokehouse BBQ (Englewood, CO) 
Texas Dip (brisket & sausage on Texas Bread)....$6.75
 
J.J.Bitting Brewing Co. (Woodbridge, NJ)
JJ Bitting Brewing Company
33 Main Street
Woodbridge, NJ 07095
(732) 634-2929
(...)
I had their Texas Dip which was like a french dip only made with Prime Rib, excellent. 
 
Tex Wasabi’s (Santa Rosa, CA)
Texas-Dip $8-1/2
Marinated & thinly sliced roast beef with jalapeno jack, creamed horseradish & some dynamite au jus on a soft french roll. One of the best dips you’ll ever try.
 
Waterfront Ale House (NYC)
HEARTY SANDWICHES:
TEXAS DIP Tender Smoked Beef Brisket on Toasted French Bread with Barbeque Dipping Sauce
 
Tom’s Ribs (San Antonio, TX)
SANDWICHES
TEXAS DIP ....... Thinly sliced brisket on a hoagie bun with BBQ sauce, topped with Swiss cheese. Served with spicey au jus.
 
Boathouse Rotisserie (Chattanooga, TN)
“Texas Dip” Brisket with Swiss, Onions, & Au Jus to Dip
 
Hooters Texas
Texas Dip Sandwich