Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente. Reserve 1/2 cup water and drain.
Warm olive oil and butter in a wide skillet over medium heat.
Sauté garlic and red pepper flakes for 30–60 seconds until fragrant, not browned.
Stir in tomato paste and cook 2–3 minutes to deepen the color and flavor.
Pour in crushed tomatoes. Simmer gently for 5–7 minutes, stirring occasionally.
Lower heat and add heavy cream. Season with salt and black pepper. Simmer until slightly thickened, 2–3 minutes.
Toss cooked pasta into the sauce. Splash in reserved pasta water as needed to loosen and coat.
Take off heat and fold in Parmesan until glossy. Finish with basil. Taste and adjust seasoning.