Melt butter in a large saucepan or small Dutch oven over medium heat.

Add diced onion, sliced garlic, and red pepper flakes; season lightly with salt and cook, stirring frequently, until onions are very soft and not browned, about 15 minutes (reduce heat if needed).

Stir in tomato paste and cook, stirring, until fragrant and slightly thickened, about 3 minutes.

Add the canned whole peeled tomatoes with their liquid, bring to a simmer, and simmer, crushing the tomatoes roughly with a spoon, until the sauce thickens slightly, about 10 minutes.

Stir in the whipping cream, then transfer the sauce to a blender and blend until very smooth (or use an immersion blender if safe to do so). Return the blended sauce to the pot and season lightly with salt.

Bring a pot of salted water to a boil and cook the pasta until about 3 minutes shy of package directions (just shy of al dente). Reserve pasta water.

About 1 minute before adding pasta, add the vodka to the tomato sauce and bring to a gentle simmer over medium heat.

Using a spider or slotted spoon, transfer the pasta directly to the sauce along with 1/2 cup (120 ml) of reserved pasta water (or add drained pasta plus 1/2 cup reserved water). Increase heat and cook, stirring constantly, until pasta is well coated and reaches al dente, about 3 minutes; add more pasta water 1/4 cup at a time if sauce becomes too thick.

Remove from heat and stir in the grated Parmigiano-Reggiano until the sauce is smooth and creamy. Taste and adjust salt; add a few drops more vodka if desired (use sparingly).

Spoon pasta onto warmed plates, top with additional grated cheese, and serve immediately.