Bring a large pot of salted water to a boil, add pasta, and stir. Cook pasta until it is al dente, about 7 minutes.
Carefully, remove 1 ¼ cups of the hot pasta water and set aside.
Drain the al dente pasta, return it to the empty pot, drizzle with a little olive oil, stir, and set aside. *This step will prevent the pasta from sticking while preparing the vodka sauce.
Place a large skillet over medium heat. Once the skillet is hot, add the olive oil and sauté the shallots and garlic for 3 to 4 minutes, until the shallots are soft and translucent.
Add tomato paste and stir together with the shallots and garlic. Continue to stir until the paste turns bright red, 2 to 3 minutes.
Deglaze the skillet with vodka, stirring until the vodka evaporates. Lower the heat if needed.
Add the reserved pasta water to the skillet and stir it in with the tomato paste until smooth, about 1 minute.
Add the butter to the skillet and stir until melted into the sauce.
Stir the cream into the sauce until smooth. Reduce the heat to low and simmer together, about 3 to 4 minutes. Add the Parmesan cheese, stir, and simmer until the sauce is smooth, glossy, and has thickened enough to coat the back of a spoon, about 3 minutes. Season with salt and pepper.
Add cooked pasta a little at a time to the sauce and mix until fully coated.
Serve with additional grated Parmesan, chopped parsley and red pepper flakes.