Preheat oven to 400 degrees. Bring a large pot of water to a boil; add salt. Add pasta; cook until slightly underdone. Drain, rinse in cold water, and drain. Toss pasta with 1 tablespoon oil to coat. Set aside.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add meat. Cook, stirring occasionally, until browned, about 10 minutes. Add garlic, 1 teaspoon salt, and pepper. Cook 2 minutes more. Add tomatoes; simmer until thickened, about 20 minutes.
Butter a 9-inch springform pan. Toss pasta with Parmesan cheese. Tightly pack pasta into pan, standing each piece on end.
Spread 2 cups meat sauce on top of pasta, pushing it into holes. Bake 15 minutes. Sprinkle mozzarella on top. Bake until cheese is pale golden, 10 to 15 minutes more. Remove from oven, and let stand 15 minutes. Run a knife around edge to loosen; unmold. Cut into wedges. Serve with remaining sauce.