Boil the pasta: Bring a large pot of salted water to a rolling boil.
Cook pasta until just shy of al dente. Reserve 1/2 cup pasta water before draining.
Sauté aromatics: In a large skillet over medium heat, warm olive oil and butter. Add shallot and a pinch of salt; cook 2–3 minutes until soft.
Stir in garlic and red pepper flakes; cook 30–60 seconds until fragrant.
Add tomatoes: Pour in tomato puree. Simmer 3–4 minutes to reduce slightly and mellow the acidity. Taste and season with salt and pepper.
Make it pink: Lower the heat and stir in the cream.
The sauce should turn a rosy color. Let it gently bubble for 1–2 minutes, stirring, until silky.
Cheese and water: Sprinkle in Parmesan and a splash of pasta water. Stir until the cheese melts and the sauce looks glossy.
Add more pasta water as needed to reach a lightly creamy, clinging consistency.
Combine: Add the drained pasta to the skillet and toss for 1–2 minutes so it finishes cooking in the sauce. Adjust salt and pepper. If using, add a touch of lemon zest for brightness and torn basil.
Serve: Plate immediately with extra Parmesan and a crack of black pepper.