Cook and stir beef, onion, and garlic until brown; drain. Stir in sauce, mushrooms, sugar, oregano, basil, salt, and pepper. Heat to boiling, stirring constantly; reduce heat. Simmer, stirring occasionally, 10 minutes. Heat oven to 400°F. Grease baking dish, 8 x 8 x 2 inches.
Mix baking mix, milk, and egg; spread half in pan. Top with 4 cheese slices. Spoon beef over cheese. Top with remaining cheese slices; sprinkle with Parmesan cheese. Drop remaining dough by spoonfuls onto cheese. Sprinkle with paprika if desired. Bake until light brown, about 20 minutes.