Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve one cup of the cooking water, then drain the pasta. Drizzle lightly with olive oil, toss and set aside. Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the shallot and cook, stirring, until soft, about 2 minutes. Add the tomatoes, vodka, the reserve cooking water, half teaspoon salt and the red pepper flakes. Bring to a rapid simmer and cook, stirring occasionally, until slightly thickened, About 12 to 15 minutes. Stir in the cream and simmer one more minute.

Add the cooked pasta, the remaining 1 tablespoon olive oil, the grated cheese and parsley to the sauce. Cook, tossing, 2 to 3 minutes. Season with salt. Divide among bowls and top with more cheese.