Bring a large pot of salted water to a boil. Cook rigatoni according to package instructions until al dente. Reserve 1 cup of pasta water before draining.
Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add the ground beef and cook until browned, about 5 to 7 minutes. Remove the beef from the pan and set aside.
In the same skillet, lower the heat to medium. Add the finely chopped white onion and sauté until softened, about 5 minutes. Stir in the minced garlic and Calabrian chili paste, cooking for 1 additional minute.
Add the tomato paste to the skillet. Cook, stirring frequently, until the paste darkens to a deep red color, roughly 5 minutes.
Reduce the heat to low. Slowly whisk in the heavy cream and unsalted butter until the mixture forms a smooth, rich sauce.
Stir the browned beef back into the sauce. Add the cooked rigatoni and toss vigorously to coat. Pour in reserved pasta water, 1/4 cup at a time, until the sauce reaches your preferred consistency.
Remove from heat. Stir in the grated Parmigiano-Reggiano and fresh chopped basil. Serve immediately.