Bring a large pot of water to a boil. Salt and cook pasta until al dente, or according to package instructions. Reserve 1/2 cup pasta water. Drain and set aside.
In a large skillet over medium-high heat, saute the shallots in olive oil just until translucent, about 3 minutes. Add garlic, tomato paste, and crushed red pepper flakes, stirring until combined, about 3 minutes.
Add vodka and stir well to incorporate, scraping the bottom of the pot.
Turn heat to low and stir in heavy cream, reserved pasta water until smooth. Remove from the heat.
Add the cooked pasta and season with salt and black pepper. Toss well to combine. Plate and sprinkle grated parmesan cheese, chopped basil, and a pinch of crushed red pepper flakes. Serve immediately.