Bring a medium saucepan of salted water to a boil. Add the pasta and cook until just al dente, 5 to 6 minutes. Drain in a colander and return to the saucepan.
Meanwhile, in a large skillet, heat the olive oil over medium heat. Add the sausage and cook, stirring, until browned and all pink has disappeared, 3 to 4 minutes. Add the onions, salt, and red pepper flakes and cook, stirring, until the onions are soft and golden, about 5 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the tomatoes and cook, stirring, until thick, about 2 minutes. Add the vodka and cook until the sauce reduced by half, 3 to 4 minutes. Stir in the cream and cook until the sauce thickens, about 2 minutes. Stir in the basil and remove from the heat.
Toss the sauce with the pasta to coat evenly and transfer to a pasta bowl for serving. Top with cheese and sprig of basil and serve immediately.