Few American dishes are more comforting than Brunswick stew, a motley mix of tomatoes, corn, beans and shredded meat. Chicken is most commonly used today, though some stew experts throw in beef chuck or pork shoulder for flavor and fat (or they prepare it in the old way, using game meat such as squirrel and rabbit). Both Brunswick County, Va., and Brunswick, Ga., lay claim to this hearty fall stew. This version borrows from the sweet and savory Virginian tradition. Thickened with potatoes…