A “Basque barbecue” is a lamb barbecue. A significant number of sheepmen (mostly in California and Nevada) were from the Basque region. The Basque barbecue dates to at least the early 1930s.
1 May 1932, Fresno (CA) Bee, “Sheepmen Gather At Mendota For Annual Picnic,” pg. 6A, col. 5:
Basques and Frenchmen, Italians and Spaniards—all Americans—for the annual field day and picnic of the San Joaquin Valley Wool Growers’ Association.
(...)
Thirty lambs, which had been provided by A. J. Arnauden, Jr., at whose place the picnic was held, were barbecued according to accepted custom by A. Flores of Hanford and J. R. Flores and Toney Naves, also of Hanford.
26 April 1936, Fresno (CA) Bee, “Valley Sheepmen Attend Annual Picnic at Huron,” pg. 2D, col. 1:
...sheepmen had donated seventy-five of their choicest lambs, and a corps of cooks barbecued 3,000 pounds of meat in the approved Basque style.
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Sheepmen and their families from all parts of the valley, most of them sturdy Basques from the Spanish and French Pyrenees, took the occasion to meet friend whom they had not seen since last year’s picnic and to swap the latest gossip and talk over the price of veal and lambs.
9 May 1948, Fresno (CA) Bee, “Valley Wool Growers Hold Annual Picnic,” pg. 3, col. 1:
Between 80 and 90 prime Spring lambs, amounting to about 4,000 pounds of meat, were barbecued in the traditional Basque manner by a crew of sheepmen under the direction of Frank Zubeldia, Jr., of Lemoore.
Roundup Recipes
by Bonnie & Ed Peplow
with the help of the Arizona Cowbelles
Cleveland, OH: The World Publishing Company
1951
Pg. 263 (Glossary):
BASQUE BARBECUE: A lamb barbecue. Named because a significant percentage of sheepmen in the Southwest are of Basque ancestry.
22 June 1954, Reno (NV) Evening Gazette, pg. 6, col. 7:
More than 2000 sampled Chef Paul Breinholt’s basque barbecue at the fourth annual fair sponsored by the Washoe Medical Center women’s league held Saturday at Pickett Park. Chef Breinhold arrived on the scene at 4 a.m. to prepare the five lambs for their six hour barbecue over hot coals.
5 October 1961, Nevada State Journal (Reno, NV), pg. 11, col. 1 photo:
LEGISLATORS AT BASQUE BARBECUE
Hundreds of visiting legislators watched visiting Basque contests as part of the Basque barbecue held on the lawn of the Capitol Building in Carson City Tuesday.
3 May 1964, New York (NY) Times, pg. XX35:
NEVADA
Basque Barbecue, Ely, July 18-19.
Google Books
The Dictionary of American Food and Drink
by John Mariani
New Haven, CT: Ticknor & Fields
1983
Pg. 28:
Basque barbecue. A barbecue made from lamb, so called by cowboys because many nineteenth century sheepmen were of Basque ancestry.
Google Books
Dictionary of the American West:
Over 5,000 terms and expressions from Aarigaa! to Zopilote
by Win Blevins
Seattle, WA: Sasquatch Books
2001
Pg. 19:
BASQUE BARBEQUE A lamb barbeque; a barbeque where the eaters are Basques, who are often sheepmen.
East Oregonian (July 8, 2007)
Mario brings Basque grilling to region
By George Murdock
The East Oregonian
(...)
Mario came to Eastern Oregon from Pamplona, Spain, in 1959. His Basque barbecue went through various stages from “head logging camp cook” to the occasional weekend backyard barbecue to the tasty business it has become today.
The secret behind his success appears to be the marinades he concocts for red meat, poultry and fish coupled with his professional grilling techniques.
Much of his claim to fame probably came from his penchant for charbroiling lamb. Some would say nobody converts more non-believers to lamb than Mario. In fact, he always has promoted the lamb market by offering his very exclusive, signature Lamb K-Bobs.