Prepare the pasta: Bring a large pot of generously salted water to a boil. Cook rigatoni according to package instructions until al dente. Remember to reserve 1/4 cup of pasta water before draining.
Make the sauce base: Heat olive oil in a large skillet over medium heat. Add minced garlic and sauté for about 30 seconds until fragrant but not browned. Add tomato paste and hot pepper paste, stirring continuously for 2-3 minutes until slightly darkened and caramelized.
Create the creamy sauce: Reduce heat to medium-low and slowly pour in the heavy cream while stirring constantly to create a smooth sauce. Add dried basil, red pepper flakes, Italian seasoning, black pepper, and salt. Simmer for 5 minutes, allowing the flavors to meld together.
Incorporate the cheese: Gradually add the parmesan and pecorino romano cheeses to the sauce, stirring until completely melted and the sauce is smooth and velvety.
Combine pasta and sauce: Add the cooked rigatoni to the sauce along with butter and reserved pasta water. Toss thoroughly until each piece of pasta is well-coated with the creamy sauce. The starchy pasta water and butter will help the sauce cling to the pasta.
Finish and serve: Allow the pasta to cook in the sauce for another 1-2 minutes. Taste and adjust seasoning if necessary. Serve immediately, garnished with additional cheese if desired.