Add tomato paste to pot and cook, stirring occasionally, until thickened slightly and darkened in color, 2 to 3 minutes. Pour in tomatoes along with their liquid and the vodka, scraping up any browned bits on the bottom of the pot. Bring to a simmer.

Cook, breaking up tomatoes, until sauce has thickened and tomatoes have broken down, about 10 minutes. Remove from heat and stir in heavy cream until fully incorporated.

Use an immersion blender or pour sauce into a traditional blender and blend until smooth. Return sauce to pot.

Add 2 tablespoons salt to a large pot of boiling water and add pasta. Cook until al dente according to package directions. Reserve 1½ cups pasta water before draining.

Return sauce to a simmer over medium-low heat. Add ½ cup pasta water and Parmesan and stir until incorporated. (For a smoother sauce, add pasta water ¼ cup at a time until you reach your desired consistency.) Season to taste with salt.

Add reserved cooked onion mixture and pasta to sauce and toss until fully coated and heated through.

Serve immediately with a light dusting of Parmesan.