Heat oil in large nonstick skillet over medium heat. Add beef, onion, green pepper and garlic; sauté, breaking up clumps of beef with wooden spoon, for 8 minutes. Add the tomatoes, tomato paste, water, chili powder, salt and ground red pepper. Bring to boiling. Reduce the heat to low; simmer, uncovered, for 30 to 35 minutes. Stir in the drained kidney beans.
Fill each phyllo shell with scant tablespoon chili. Top with sour cream and Cheddar.