Adjust oven rack to middle position and heat oven to 400 degrees. Bring 4 quarts of water to boil in dutch oven oven high heat. Stir in 1 tablespoon salt and pasta; cook, stirring occasionally, until al dente. Reserve 1/4 cup of cooking water. Drain pasta, return to pot and toss with 1 tablespoon of oil; set aside.
While the pasta is cooking, heat remaining 2 tablespoons oil and garlic in meduim skillet over medium heat until fragrant but not brown, about 2 minutes. Stir in tomatoes and simmer until thickened slightly, about 10 minutes. Off heat, stir in basil and season with salt and pepper to taste.
Add tomato sauce and reserved pasta-cooking water to pasta; stir to combine. Pour half (about 4 cups) of pasta into 9 by 13 inch baking dish. Sprinkle with half mozzarella and half Parmesan. Pour remaining pasta into dish and sprinkle with remaining mozzarella and Parmesan. Cover with foil and bake until cheese melts, about 15 minutes. Remove foil and continue to bake until cheese begins to brown, about 5 minutes. Serve immediately.