Bring a large pot of lightly salted water to a boil. Cook pasta according to package instructions. When draining, reserve about ½ cup of pasta water.
While pasta is cooking, add olive oil to a large skillet over medium heat. When hot, add shallot or onion and cook until it begins to soften, about 5 minutes. Add garlic and cook until fragrant, about one minute.
Add tomato paste and stir. Let cook for 3-4 minutes until it's starting to brown/caramelize a bit.
Stir vodka into sauce and let cook for about 1 minute.
Add heavy cream, red pepper flakes, salt, and pepper and stir to combine. Remove from heat.
Add cooked pasta, reserved pasta water, and butter to skillet and toss to coat pasta in sauce. Stir in parmesan cheese.
Serve pasta topped with additional parmesan and chopped basil.