Preheat broiler to high. Heat 3 tbsp. oil in a 2- to 3-qt. saucepan set over medium heat, then add tomatoes and oregano and simmer, uncovered, for 15 minutes.
Meanwhile, in a large frying pan, heat 1 tbsp. oil over medium-high heat. Add onion, bell pepper, garlic, salt, pepper, and chile flakes, and stir to combine. Cover pan, lower heat to medium, and cook until vegetables soften, about 5 minutes. Add sausage, stirring and breaking it into small pieces with a wooden spoon as it firms up, about 5 minutes. Cover pan and cook until vegetables are tender and sausage is cooked through, 5 to 8 minutes more. Add tomato sauce and simmer 10 minutes.
While sauce is cooking, pour remaining 1 1/2 tbsp. oil into a 9- by 13-in. baking pan and tilt to coat bottom. Add polenta slices to pan and turn to coat with oil, then arrange slices lengthwise in 3 slightly overlapping rows. Broil polenta about 4 in. from heating element until golden brown and crispy, 10 to 15 minutes.
Pour sauce over broiled polenta, then arrange mozzarella slices over the top. Broil until cheese is melted and beginning to brown, about 2 minutes. Let cool slightly before serving.
Note: Nutritional analysis is per serving.