Preheat oven to 400 degrees. Grease a 9-inch-by-13-inch baking dish with olive oil. In a large stockpot, bring 4 quarts water and 1 tablespoon salt to boil. Add pasta and cook according to package directions for al dente, about 10 minutes. Drain well.
In a medium saucepan over medium-high heat, heat oil until shimmering. Add garlic cloves and sauté until browned, stirring occasionally to prevent scorching, about 3 to 4 minutes. Remove garlic and discard. Add sausage and cook until just starting to brown, breaking up clumps with a wooden spoon, about 3 minutes.
Stir in crushed tomatoes, diced tomatoes, sugar, basil, oregano, and salt and pepper to taste (I like 1/2 teaspoon salt and 1/4 teaspoon pepper). Simmer uncovered, stirring occasionally, about 10 minutes.
To the sauce, add the cooked pasta and stir to combine. Add cubed mozzarella, Parmesan cheese, 1/2 teaspoon freshly ground black pepper, and crushed red pepper (if using) and stir to combine. Pour into the prepared baking dish.
Cover the top of the pasta with the sliced mozzarella and sprinkle evenly with the remaining Parmesan. Bake until lightly browned and hot, about 30 minutes. Garnish with parsley and serve.