Preheat the oven to 425°F and set the oven rack in the middle position.
In boiling salted water, cook the pasta to very al dente according to the package directions, about 7 minutes. Drain and add the pasta back to the pot. Set aside.
Heat oil in a sauté pan over medium high heat, then cook and crumble the sausage until no pink remains.
Use a slotted spoon to transfer the cooked sausage to a plate. Drain all but 2 tablespoons of the fat from the pan.
Sauté the garlic briefly and add the tomatoes, salt, sugar, and red pepper flakes. Simmer uncovered for 10 minutes.
Add heavy cream, 1/3 cup of the Pecorino Romano, cooked sausage, and basil to the pan; stir until evenly combined. Add cooked pasta and stir.
Spoon half of the mixture in a 9 x 13-inch baking dish. Sprinkle with half of the shredded mozzarella and half of the remaining Pecorino Romano.
Spoon remaining pasta mixture on top and sprinkle with the remaining mozzarella and Pecorino Romano.
Bake uncovered until cheese is melted and browned, 15 to 20 minutes.