Bring a large pot of salted water to a boil and cook the rigatoni according to package directions until al dente. Reserve 1/2 cup of pasta water before draining. While the pasta cooks, add the blended cottage cheese to a small bowl—I blend mine until completely smooth to ensure a silky sauce texture without any lumps. Set both aside until needed.
In a large skillet over medium heat, melt the butter and add the finely minced shallots. Cook for 3-5 minutes, stirring frequently, until they're softened and just beginning to turn golden—this develops their sweetness and eliminates any harsh onion bite. Add the minced garlic and cook for another 30 seconds until fragrant, then stir in the tomato paste. Cook the tomato paste for 2-3 minutes, stirring constantly to deepen its color and cook off any raw tomato flavor, which concentrates and enriches the sauce.
Pour in the vodka and cook for 3-4 minutes, stirring occasionally, to allow the alcohol to evaporate and its subtle flavor to meld into the sauce. I find that this step rounds out the acidity of the tomatoes and adds a sophisticated depth that's signature to vodka sauce.
Reduce heat to medium-low and slowly stir in the blended cottage cheese from Step 1, letting it warm through without boiling. Add the chili flakes and freshly grated Parmesan cheese, stirring gently until the cheese melts and the sauce becomes silky and cohesive. Season with salt and pepper to taste, keeping in mind the Parmesan will add saltiness, so taste as you go.
Add the cooked pasta from Step 1 to the sauce and toss gently to coat every piece. If the sauce seems too thick, add the reserved pasta water a splash at a time until you reach a creamy consistency that lightly coats the pasta. Divide into bowls and garnish generously with fresh basil and additional Parmesan if desired.