Bring 4 quarts of water to boil in the 8-quart pot. Preheat the oven to 400° F.
Add the olive oil to the nonstick pan and saute garlic for about 2 minutes, until soft and fragrant. Add the tomatoes and juices. Stir and bring to a simmer over low heat until slightly thickened, about 15 minutes. Stir in the basil, sugar, and ½ teaspoon kosher salt and turn off the heat.
Add 1 teaspoon kosher salt and the pasta to the boiling water. Bring back to a boil, stirring frequently. Cook just until the pasta starts to get tender, but is still a little firm, not quite al dente. If you cook the pasta too long, it will be mushy after baking.
Set aside ½ cup of the pasta water and drain the rest. Return the pasta to the pot and add the tomato sauce. Stir together well. Add as much of the reserved pasta water as is needed to thin the sauce a bit.
Build the dish in layers. Start with half of the pasta and sauce to the bottom of the pan, then sprinkle half the cheeses on top. Layer on the rest of the pasta and sauce, and sprinkle the remaining cheese on top.
Bake about 20 minutes, or until the cheese turns golden brown. Let stand 5 minutes, then serve.