Heat 1 tablespoon oil in medium skillet over medium heat. Add onion; sauté 5 minutes. Add garlic; sauté 1 minute. Add corn; sauté until heated through, about 3 minutes. Remove from heat.
Bring 2 cups water and 1 teaspoon salt to boil in medium saucepan over medium heat. Whisk cornmeal and 1 cup water in medium bowl to blend. Whisk cornmeal-water mixture into boiling water; return to boil. Cook until polenta is smooth and thick, stirring often, about 30 minutes. Stir in corn mixture.
Brush 11x7x2-inch dish with oil. Spread polenta in dish. Cool completely. (Can be made 1 day ahead. Cover; chill.)
Prepare barbecue (medium-high heat). Brush grill with oil. Cut polenta into 12 squares. Brush both sides with oil. Place on grill; cover grill. Grill until polenta is golden brown, about 3 minutes per side, sprinkling with cheese during last minute. Serve hot.