Bring a large pot of salted water to a boil for the pasta. In a large skillet over medium heat, melt the butter in the olive oil. Add the diced onion and crushed garlic. Let the onion and garlic sweat a few minutes, without coloring; then, in a hot spot, add the crushed red pepper. Let it toast for a minute. Ladle in about ½ cup pasta water, and simmer to break down the onion, about 2 to 3 minutes.

Once the onion has softened, add the crushed tomatoes, slosh out the can with about a cup of water, and add that, too. Season with salt. Bring to a simmer, and cook until thickened, about 10 to 12 minutes. When the sauce is almost done, add the pasta to the pot of boiling water and stir.

Once the sauce has thickened, remove the garlic cloves, and add the half-and-half and vodka. Bring to a boil, and cook until the sauce comes together and thickens again, about 3 minutes. When the pasta is al dente, scoop it out of the pot with a strainer or spider and add directly to the sauce. Cook and toss the pasta in the sauce until all of the pasta is coated with the sauce. Off heat, toss with the grated cheese and basil. Serve immediately.