Steel Knife: With machine running, drop chili through feed tube and mince. Remove from work bowl.
Shredder: Arrange cheese in feed tube and shred using light pressure.
Generously grease 8-inch square pan. Bring water, 2 tablespoons oil and the salt to boil in large heavy saucepan. Reduce heat to low. Add cornmeal in thin, steady stream, whisking constantly. Cook until mixture is very thick and film forms on bottom of pan, stirring frequently, about 9 minutes. (Or to microwave: Combine water, 2 tablespoons oil, salt, and cornmeal in 3-quart microwave casserole. Cover and cook on High 4 minutes. Uncover; whisk until smooth. Cover and cook until very thick, about 6 minutes.) Add chili, half of cheese and pepper and stir until smooth. Transfer mixture to prepared pan. Smooth top with spatula. Cool completely. (Can be prepared 3 days ahead. Cover and chill.).
Position rack in center of oven and preheat to 425 degrees. Grease large baking sheet. Cut polenta into eight rounds using 2 1/2-inch biscuit cutter. Transfer to prepared sheet. Brush tops of rounds with remaining 1 tablespoon oil. Sprinkle with remaining cheese. Bake until cheese is golden, 10 to 12 minutes. (Or to microwave: Arrange 4 polenta rounds in circle on microwave plate. Brush with oil and sprinkle with cheese. Cook uncovered on Medium 7 minutes. Repeat with remaining polenta, oil, and cheese. Serve hot.