Preheat oven to 350°. In a 6-qt. stockpot, cook rigatoni according to package directions. Drain; transfer to a bowl.
In same stockpot, cook and crumble sausage with red pepper and onion over medium heat until meat is no longer pink. Add garlic; cook 1 minute longer. Drain. Add cream; cook 5 minutes, stirring occasionally. Stir in tomatoes, tomato paste, Italian seasoning and pepper flakes. Cook, uncovered, over medium-low heat until sauce thickens slightly, 5-8 minutes. Meanwhile, combine ricotta, 1/2 cup Parmesan, goat cheese, egg and seasonings.
Stir rigatoni into meat sauce. Spread 3 cups into each of two greased 11x7-in. baking dishes. Top each with half of cheese mixture, then half of remaining pasta mixture.
Bake, covered, 25 minutes. Sprinkle with mozzarella and remaining Parmesan cheese. Bake, uncovered, until cheeses are melted, about 5 minutes. If desired, sprinkle with basil.