New Mexico may appear to be the land of a thousand Margaritas, but its distilleries and historic cocktails are complex enough to satisfy even the most discerning palate. Cowboys and banditos alike distilled and drank their way to infamy. Prohibition drinkers masked the questionable spirits with cocktails at local joints like the legendary triple-level speakeasy of Santa Fe that was so secret, it had no name. Though the state had no legal distilleries for several decades following Prohibition, Arturo Jaramillo created the quintessential New Mexican cocktail in 1965. When Don Quixote Distillery...