Pat Martin is one of a rare breed: an open-pit barbecue master who uses whole hogs, a West Tennessee tradition that requires a 24-hour cooking time at 200 degrees Fahrenheit—as well as hours of prep. “The French have their cheese; we as Americans have our barbecue. You drive 50 miles and it changes,” Martin said. Born in Memphis, he first remembers a trip to Gridley’s Bar-B-Q when he was 5 years old. His father’s job took them to the East Coast for several years, but then they moved to Mississippi to be near family. In high school, Martin bought his first cookbook, “The Thrill of the Grill.” A section about whole-hog barbecue “really filed itself away in my brain,” he said. During his first week at college in 1990, he found Thomas & Webb Barbecue, and it was “an absolute epiphany,” he said. Owner Harold Thomas personally put together his …