Cook meatballs according to package instructions and allow them to rest.
Bring a large pot of water to a boil and cook pasta according to package instructions.
While pasta is cooking, heat a heavy-bottomed pot (large enough to hold the pasta and meatballs with room to spare), add the olive oil, and sauté the shallot and garlic until softened.
Add the tomato paste and crushed red pepper to the pot and cook for about 2 minutes, stirring constantly.
Deglaze the pot with the vodka, bring to a boil, then add the crushed tomatoes and cream, stirring frequently.
Drain the pasta, reserving about 2 cups of the pasta water.
Once the sauce has come to a boil, adjust to desired consistency with the pasta water.
Toss the pasta, meatballs, butter, and about half of the parmesan cheese with the sauce, combining well.
Transfer the pasta to a large serving platter or bowl, sprinkle with the remaining cheese and the basil.