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 eight 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.
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 and basting patties with 2 tablespoons reduced vinegar after turning. If prepared polenta is not available, the following may be used: Combine 3 cups water, 1 tablespoon butter and 1/2 teaspoon salt in large saucepan and bring to a boil. Gradually whisk in 1 cup cornmeal. Reduce heat to medium-low; cook 15 minutes, stirring often. (Mixture will be very thick.) Remove from heat; cool slightly. Spoon polenta on aluminum foil-line baking sheet. Cover with plastic wrap and pat into 12 by 6 by 1/2-inch rectangle. Refrigerate 1 hour or as long as overnight. Cut chilled polenta into 8 (3-inch) circles using a cookie or biscuit cutter. Proceed as directed above. Prepared balsamic syrup, available in large supermarkets and specialty food stores, may be substituted for balsamic reduction.
Recipe courtesy of American National CattleWomen, Inc. created by Osceola Mills, Pennsylvania