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.