Warm the olive oil in a sauté pan over medium heat. Add the diced onion, minced garlic, 1/4 teaspoon salt, and crushed red pepper flakes.
Cook for 2–3 minutes, stirring from time to time, until the onion becomes tender and the garlic is aromatic.
While the aromatics cook, fill a large pot with 4–5 quarts of water and season it with the tablespoon of salt. Place the pot over heat and bring the water to a boil as the sauce is prepared.
Add the tomato paste, canned tomatoes, and chopped basil to the sautéed onion and garlic mixture.
Stir until thoroughly combined, then cook for approximately 5 minutes. Stir regularly so the tomato mixture does not adhere to the bottom of the pan.
Transfer the cooked tomato mixture to a blender and add the cottage cheese.
Blend on high speed for 1–2 minutes, or until completely smooth, creamy, and free of visible lumps. Set the blended sauce aside.
Add the rigatoni to the boiling water and cook according to the package directions until al dente.
While the pasta cooks, clean the sauté pan and return it to the stovetop over low to medium heat. Pour the blended tomato-cottage cheese sauce back into the pan, then stir in the 1/2 cup grated Parmesan.
Heat gently, stirring occasionally, until the Parmesan has melted smoothly into the sauce.
Pour in the vodka and allow the sauce to simmer for roughly 2 minutes so that some of the alcohol cooks off.
Drain the al dente rigatoni thoroughly and transfer it directly to the pan containing the simmering vodka sauce.
Stir and toss until every piece of pasta is evenly coated with the creamy tomato sauce. Serve hot with the additional grated Parmesan as garnish.