Start water for pasta in a pot and add a liberal quantity of salt. When boiling, toss the rigatoni in. In the meantime, start work on the sauce.
Add olive oil to a dutch oven over medium heat. Chop shallots and garlic very finely and add to the pan with oil. Cook until browning at the edges, 5 or 6 minutes. Once the shallots begin to brown, add the tomato paste and red pepper. Cook this until the paste darkens slightly and sticks to the bottom.
Deglaze the pan with the vodka. Be sure to scrape the bottom of any dark burned bits. As this is boiling, scoop ¼ cup of the pasta water into a bowl and add ¾ cup heavy cream. The pasta water brings the cream up to temperature so that it will not scald when added to the hot pan.
Reduce the heat to low and slowly stir the cream in. Once the cream is in, add half the grated parmesan a bit at a time while stirring, allowing it to melt into the mix. Then add another half cup of pasta water a bit at a time, stirring the whole time. This thins the sauce. If you’d like the sauce a bit thinner, you can keep adding water a bit at a time, but probably no more than another quarter cup.
Serve the pasta topped with the remaining parmesan cheese, a few cranks of black pepper, and a bit of chopped fresh basil.