Preheat charcoal grill to medium heat.
Bring vinegar to a boil in a 2-quart saucepan. Reduce heat; simmer, uncovered, 9 to 10
minutes or until reduced to 1/3 cup. Set aside.
Meanwhile lightly shape ground beef into 8 (1/2-inch) thick patties.
Brush polenta slices with oil. Place patties in center of grill over medium, ash-covered coals and arrange the polenta around the patties. Grill patties and polenta, uncovered, 11 to 12 minutes or until patties are medium (160 degrees F) doneness, not pink in center and juices show no pink color and polenta is heated through, turning once and basting patties with 2 tablespoons reduced vinegar after turning. Season burgers with salt and pepper, to taste.
For each serving, layer 1 each polenta slice, burger, mozzarella slice and tomato slice.
Drizzle with remaining vinegar and sprinkle with basil, as desired.
Cook's Tip: To cook over a gas grill, preheat grill according to manufacturer's directions for medium heat. Grill patties and polenta, covered, 9 to 10 minutes or until patties are medium (160 degrees F) doneness, not pink in center and juices show no pink color and polenta is heated through, turning once