Bring a large pot of water to a boil and season it generously with kosher salt. Add the rigatoni and cook until 2 minutes less than al dente. Reserve 1 cup of the starchy pasta water, then drain the pasta and set it aside.
While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the Italian sausage, breaking it into bite-size crumbles. Cook for 8 to 10 minutes, stirring occasionally, until browned and cooked through. Transfer the sausage to a plate, leaving a little of the fat in the pan.
In the same skillet, add the marinara sauce, heavy cream, Calabrian chili paste or crushed red pepper flakes (if using). Stir and bring to a gentle simmer over medium heat.
Stir in 1/2 cup of the Parmesan cheese until melted and the sauce is smooth.
Add the drained rigatoni and browned sausage to the skillet. Toss gently until evenly coated. If the sauce is too thick, add reserved pasta water, a splash at a time, as needed. The mixture should look slightly saucier than you want the finished bake, since the pasta will absorb some of the sauce in the oven.
If using a separate baking dish, lightly oil a 9 × 13-inch baking dish. Transfer the rigatoni and sausage to the prepared dish, or leave it in the skillet if oven-safe. Top with the mozzarella and the remaining 1/4 cup Parmesan, then drizzle with olive oil.
Loosely cover the dish with foil. Bake at 400°F for about 15 minutes.
Remove the foil and bake for another 5 to 8 minutes, or until the pasta is bubbling around the edges and the top is melted and lightly golden.
Remove from the oven and let the pasta rest for a few minutes. Top with torn fresh basil, if desired, and serve.