Bring a large pot of well-salted water to a boil.

Meanwhile, in a large saucepan over medium-high heat, heat the garlic and red pepper flakes in the oil until they're fragrant and sizzle steadily for about 30 seconds. Add the tomatoes and their juices and the vodka, and bring to a boil. Then reduce the heat to a steady simmer, cover with the lid slightly ajar, and cook to intensify the flavors and reduce the sauce slightly (by about one-quarter), 10 to 15 minutes.

Puree the tomatoes using a hand blender or a regular blender. If you used a regular blender to puree, return the sauce to the saucepan. Stir in 1/4 cup of the Parmigiano, the parsley, cream, salt and pepper, and more red pepper flakes if you like. Simmer to incorporate the cream and reduce the sauce slightly, about 5 minutes. Reduce the heat to low, cover, and keep warm.

Meanwhile, cook the pasta, stirring occasionally, until it's just tender to the tooth, 10 to 12 minutes. Drain well and return the pasta to its pot. Add the sauce, set the pot over medium heat, and cook, stirring, to let the pasta absorb some of the sauce, 1 minute. Serve immediately with a sprinkled with the remaining 1/4 cup Parmigiano.