Special equipment: a 9-inch springform pan
Heat 1/4 cup of the oil with the shallot in a large saucepan over medium-low heat. Once it begins to sizzle, cook the shallot, stirring occasionally, until is soft and just beginning to brown, about 6 minutes. Stir in the red pepper flakes, then add the tomatoes with their juices, vodka and 1/2 cup water. Increase the heat to high and bring the sauce to a boil, crushing the tomatoes with the back of a wooden spoon. Lower the heat to maintain a simmer and cook, stirring occasionally, until reduced and thickened, about 15 minutes. Stir in the cream, bring back to a simmer and cook for 1 minute. Remove the pan from the heat, stir in the basil and season with salt and pepper. Let the sauce cool for 10 minutes, then puree in a blender until smooth.
Preheat the oven to 375 degrees F. Grease a 9-inch springform pan with 1 tablespoon oil.
Bring a large pot of generously salted water to a boil. Cook the pasta until slightly less than al dente, about 8 minutes. Drain, spread in a single layer on a rimmed baking sheet and toss with the remaining 1 tablespoon oil.
Stand the rigatoni on their ends in the prepared springform pan until it is completely filled (you might have leftover pasta). Put the pan on a foil-lined baking sheet to catch any drips. Pour the sauce over the pasta, spreading it with the back of a spoon (you might have leftover sauce). Sprinkle with the mozzarella and Parmesan.
Cover the pan with foil, doming it slightly to avoid touching the cheese. Bake for 30 minutes. Uncover the pan and continue cooking until the top is golden brown and bubbly, about 30 minutes more. Let the pasta cool for 10 minutes, then carefully remove the sides of the pan, sprinkle with basil, cut into wedges and serve.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
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