In a large (12-inch) skillet over medium, heat 1 tablespoon oil until shimmering. Add 1 package of gnocchi to the skillet in a single layer, breaking up any gnocchi that might be stuck together. Cover (use the lid of a Dutch oven or a sheet pan if your skillet doesn’t have a lid) and cook the gnocchi undisturbed until the bottoms are golden brown, 4 to 5 minutes. Transfer to a large bowl. Repeat with 1 tablespoon olive oil and the remaining package of gnocchi and transfer to the bowl.
Heat the remaining 2 tablespoons of olive oil in the skillet over medium. Add the onion and cook, stirring occasionally, until the onion is softened and lightly golden, 3 to 4 minutes.
Add the tomato paste (reserve the now-empty can), garlic, crushed red pepper and ½ teaspoon salt, and cook, stirring frequently, until the tomato paste has darkened significantly and starts to caramelize in a few spots and stick to the bottom of the pan, about 5 minutes. Meanwhile, fill the empty tomato paste can three-quarters of the way with water and set aside.
Reduce the heat to low. Pour in the vodka and simmer, stirring and scraping up any browned bits on the bottom of the pan with a wooden spoon, until the vodka has reduced by about half, about 20 seconds.
Stir in the heavy cream, Parmesan and half of the water from the can until combined. Return the gnocchi to the pan and toss to coat in the sauce, adding more water a splash at a time as needed, until the sauce is smooth and creamy and the gnocchi is rewarmed, 1 to 2 minutes. Taste and season with salt as needed. Serve garnished with torn basil and more Parmesan.
Total Time: 35 minutes
Prep Time: 10 minutes
Cook Time: 25 minutes
