Bring a large pot of salted water to a boil. Add the penne and cook according to package directions. Drain, reserving 1 cup of the cooking water.
Whisk the yogurt with the cream in a measuring cup and set aside.
Meanwhile, heat the oil in a large skillet over medium heat. Add the shallots and 1/2 teaspoon salt and cook, stirring occasionally, until slightly softened, about 3 minutes. Add the garlic and red pepper flakes and cook, stirring, for 30 seconds. Remove from the heat and stir in the tomatoes and vodka. Return the skillet to medium heat, bring to a simmer, and cook, stirring often, until the alcohol cooks off and the sauce comes together and thickens, about 7 minutes. Stir in the yogurt-cream mixture and cook until the sauce thickens slightly, about 3 minutes.
Add the pasta, Parmesan, parsley and 1/2 teaspoon salt to the skillet and toss to combine. Use the reserved pasta water to thin the sauce as needed.
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