The exceptional thing to note about Big Boy’s Bar-B-Que is the fact that it exists at all. Located in a caliche lot along a desolate road in Sweetwater next to a bowling alley turned bar, Big Boy’s has the feel of an oasis—or a mirage. Blink and it might disappear. But Big Boy’s isn’t going anywhere. In fact, it was Harold’s, the venerable joint forty miles up the interstate in Abilene, that disappeared, back in 2011, and ever since, barbecue hounds from that city and surrounding counties have gotten used to the trek to Big Boy’s. The reward for these desert pilgrims is the meat, which is hands-down the best in the region. Travel west or northwest from Sweetwater, in an area roughly the size of Pennsylvania, and you won’t find anything that touches the plates served here. Pitmaster Gaylan Marth cooks all his meat over mesquite-fueled pits (of his own design) in a porch behind the main restaurant. The brisket, cooked for between seven and nine hours, comes out with a salty-peppery, saliva-inducing kick and will melt in your mouth and make you forget about the dusty landscape around you. Be sure to get the lean side, though. Direct heat often cooks brisket too fast to properly render the fatty end, and that’s definitely the case at Big Boy’s (as Marth himself will tell you). On the other hand, it may be just as well, since you’ll want to save room for the pork ribs. They come in two varieties, “My Ribs” and “Your Ribs.” These names originated with Mr. and Mrs. Marth. If traditional pork spareribs are your thing, order the Your Ribs (Mrs. Marth’s favorite). The My Ribs (Mr. Marth’s preferred variety) are a bit different, a country-style rib cut from pork butt. Both are served with a light candied glaze that Marth makes himself and that doesn’t overpower the flavor from the salt-and-pepper rub or the delightful smokiness in each bite. Finally, atmosphere may be incidental to the barbecue experience, but we must point out that the attractive pigskin-covered tables and chairs are imported from Guadalajara.