Place the olive oil in a large skillet and bring to a simmer over medium heat. Gently crush the garlic cloves with a large knife and peel off the papery skins. Add the garlic, crushed red pepper, and salt to the hot oil and cook, stirring occasionally, until the garlic is lightly golden, about 2 minutes. Add the tomatoes into the pan slowly and whisk well to combine. Bring sauce to a boil and simmer, stirring almost constantly, for 5 minutes. Add in the vodka and reduce the heat to a gentle simmer. Use a fork to scoop the garlic cloves out of the sauce and discard them. Add in the cream, butter, and Parmesan cheese and whisk well until they're fully incorporated into the sauce. Remove from heat, stir in gnocchi, and serve.
Place a large pot of salted water to a rapid boil over high heat. Cook gnocchi according to package instructions. Drain gnocchi and toss it in the vodka sauce. Plate, sprinkle with additional cheese and parsley, and serve at once.
