Preheat oven to 375°F (190°C). Cook pasta according to package directions. Drain and set aside.
In a large skillet, brown chorizo over medium heat. Remove chorizo and set aside, reserving some of the rendered fat in the skillet.
Add onion and garlic to the skillet and cook until softened, about 5 minutes. Stir in crushed tomatoes, heavy cream, and red pepper flakes. Bring to a simmer.
Add the cooked pasta and browned chorizo to the sauce. Stir to combine.
Pour the pasta mixture into a 9x13 inch baking dish. Top with mozzarella and parmesan cheese.
Bake for 20-25 minutes, or until the cheese is melted and bubbly.
Notes
Serve immediately. Garnish with fresh parsley, if desired.