1Heat the oil in a large saucepan over medium-high heat until shimmering. Add the garlic and shallots, season with salt and pepper, and cook until golden brown, about 4 minutes. Add the oregano and chiles and cook until fragrant, about 1 minute.
2Remove the saucepan from the heat, carefully add the vodka, scrape up any browned bits from the bottom of the pan, and stir to incorporate. Return the saucepan to the stove, reduce the heat to medium, and add the tomatoes. Cook, stirring rarely, until the tomatoes begin to collapse and let off juice, about 40 minutes. Break up some of the tomatoes with the back of a spoon, leaving some whole. Remove the sauce from the heat and discard the oregano sprigs.
3Bring a large pot of heavily salted water to a boil over high heat. Add the pasta and cook it according to the package directions. Drain the pasta, reserving 1/2 cup of the cooking water. Return the pasta to the pot and toss it with the tomato sauce and reserved cooking water until it’s well coated. Season with additional salt and pepper if necessary and serve.