Step 1

Bring a large pot of water to a rolling boil over medium-high heat; season the water generously with salt. Add the pasta and cook, stirring occasionally, until al dente, 8 to 12 minutes (depending on the pasta shape). Reserve 1 cup of cooking water in a liquid measuring cup, then drain the pasta.

Step 2

Meanwhile, heat the olive oil in another large pot or Dutch oven over medium heat. Add the shallots and cook, stirring occasionally, until just tender, 3 to 4 minutes. Add the crushed red pepper flakes, garlic and 1/4 teaspoon salt and cook, stirring frequently, until the garlic has softened, 1 to 2 minutes more. Add the tomato paste and continue to cook, stirring occasionally, until the tomato paste has turned a deep brick red and is starting to caramelize on the bottom and sides of the pot, about 6 minutes. Pour in the vodka and scrape any brown bits from the bottom of the pot, then cook until the vodka is almost completely absorbed and the alcohol has cooked off, 1 to 2 minutes. Reduce the heat to medium low, then stir in the heavy cream and 1/4 cup of the reserved pasta water until smooth and combined.

Step 3

Add the cooked pasta, Parmesan and butter to the sauce and stir to evenly combine. Taste and adjust the seasoning with more salt. Adjust the consistency of the sauce, adding 1 tablespoon of cooking water at a time, until it nicely coats the pasta (it should be creamy, glossy and saucy). Serve in shallow bowls with an extra sprinkle of Parmesan and thinly sliced fresh basil.