Bring a large pot of generously salted water to a boil. Add the rigatoni and cook 1–2 minutes less than the package instructions for al dente. Reserve at least 1 cup of the pasta water before draining.
While the pasta cooks, warm the olive oil in a large skillet over medium heat. Add the garlic and red pepper flakes, cooking 60–90 seconds until golden and fragrant. Remove from heat immediately if it starts to brown.
Stir in the tomato paste and cook 30 seconds until it darkens slightly. Add the crushed San Marzano tomatoes and stir to combine.
Simmer the sauce uncovered for 12–15 minutes, breaking up the tomatoes with a spoon, until thickened enough to coat the back of the spoon. Season with salt and pepper.
Add the drained pasta directly to the skillet. Toss over low heat, adding the reserved pasta water a splash at a time, until the sauce clings evenly with no pooled liquid.
Remove the pan from the heat. Stir in the butter until melted, then add the parmesan and toss again. Top with torn basil and serve immediately.