Boil the gnocchi: Bring a large pot of salted water to a boil. Add gnocchi and cook until they float, 2–3 minutes. Scoop them out with a slotted spoon and set aside. Reserve 1/2 cup of pasta water.

Start the sauce base: In a large skillet, heat olive oil and melt butter over medium heat. Add garlic and red pepper flakes. Cook 30–60 seconds until fragrant, not browned.

Toast the tomato paste: Stir in tomato paste and cook 1–2 minutes until it darkens slightly. This concentrates flavor and adds sweetness.

Add tomatoes: Pour in crushed tomatoes or passata. Simmer 5–7 minutes, stirring occasionally. If the sauce feels too thick, add a splash of broth or pasta water.

Creamy finish: Reduce heat to low and stir in heavy cream. Season with salt, pepper, and a small pinch of sugar if the tomatoes taste sharp. Simmer 2–3 minutes until silky.

Add cheese + basil: Stir in Parmesan until melted and smooth. Fold in most of the chopped basil, saving a little for garnish.

Combine with gnocchi: Add the cooked gnocchi to the skillet and toss gently to coat. If the sauce is too thick, loosen with reserved pasta water. If too thin, simmer a minute to reduce.

Taste and brighten: Adjust salt and pepper. Add a touch of lemon zest or a tiny squeeze of lemon if you want extra lift.

Serve: Plate in warm bowls. Top with more Parmesan, fresh basil, and a crack of black pepper. Drizzle with good olive oil if you like.