Boil the pasta: Bring a large pot of salted water to a boil.
Add the pasta and cook until just shy of al dente. Reserve at least 1 cup of the starchy pasta water, then drain.
Sauté the aromatics: In a large skillet, heat olive oil and butter over medium heat. Add garlic and red pepper flakes.
Cook 30–60 seconds until fragrant, stirring often. Do not let the garlic brown.
Build the tomato base: Stir in the tomato paste and cook for 1–2 minutes to caramelize slightly. Add crushed tomatoes and a pinch of salt and pepper.
Simmer for 5–7 minutes to thicken and mellow the acidity.
Adjust seasoning: Taste the sauce. If it’s too sharp, add a small pinch of sugar. If it needs depth, add a bit more salt or a crack of black pepper.
Add the cream: Lower the heat and stir in the heavy cream.
Start with 3/4 cup and add more if you want a richer sauce. Simmer gently for 2–3 minutes, stirring so it doesn’t scorch.
Stir in cheese and basil: Add Parmesan and most of the chopped basil, saving some for garnish. Stir until the cheese melts into the sauce.
If the sauce thickens too much, loosen it with splashes of reserved pasta water.
Combine with pasta: Add the drained pasta directly to the skillet. Toss and cook over low heat for 1–2 minutes so the pasta absorbs the sauce. Add pasta water as needed to create a glossy, silky coating.
Finish and serve: Taste and adjust with salt, pepper, and a squeeze of lemon juice if desired.
Top with more Parmesan and the remaining basil. Serve hot.