Cook the pasta.
Bring a large pot of salted water to a boil. Cook the rigatoni until al dente according to the package directions.
Before draining, reserve about 1/2 cup of the pasta cooking water. Drain the pasta and set aside.
Sauté the onion and garlic.
Heat the olive oil and butter in a large, deep skillet over medium heat.
Add the onion or shallot and cook for 2–3 minutes, or until softened. Stir in the garlic and cook for another minute, until fragrant.
Cook the tomato paste.
Add the tomato paste, jarred crushed red pepper, Italian herbs, and a pinch of salt.
Reduce the heat to medium-low and cook for 3–5 minutes, stirring frequently, until the tomato paste deepens in color. Avoid letting the garlic or paste burn.
Make the cream sauce.
Slowly pour in the heavy cream, stirring until fully combined. Bring to a gentle simmer.
Reduce the heat to low and gradually stir in the Parmesan. Cook gently for 2–3 minutes, stirring until the sauce is smooth and slightly thickened.
Add the rigatoni.
Add the drained pasta and toss until evenly coated. Stir in a splash of reserved pasta water if needed to loosen the sauce.
Cook together over low heat for another 1–2 minutes, just until the sauce clings to the pasta. Taste and adjust the salt and heat.
Serve.
Spoon into bowls and finish with fresh basil and extra Parmesan. Serve immediately.