Heat olive oil in a saucepan over medium-high heat. Add onion and salt. Cook until no longer white and starting to turn translucent, about 5 minutes. Stir in garlic; cook about 1 minute. Add red pepper flakes, then blended tomatoes with water. Bring to a simmer; adjust heat to medium or medium-low. Simmer gently, stirring occasionally, for 45 to 60 minutes. Reduce heat to low.

Bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until tender yet firm to the bite, about 8 minutes (5 minutes from doneness).

Add about 2/3 of the basil to the sauce. Stir in butter. When butter melts, add cheese in 3 increments.

Drain pasta; transfer to sauce. Stir until rigatoni are evenly coated with sauce. Serve sprinkled with the remaining basil and a dusting of grated cheese.