Step 1

In a large pot, bring 4 quarts water to a boil. Add the pasta and 1 tablespoon salt, then cook, stirring occasionally, until al dente. Reserve 2 cups of the cooking water, then drain; set aside.

Step 2

In the same pot over medium, melt 2 tablespoons butter. Add the onion, reduce to low, cover and cook, stirring occasionally, until the onion has softened, 12 to 14 minutes.

Step 3

Add the tomato paste, ½ teaspoon pepper and 1½ cups of the reserved cooking water, then whisk until smooth. Add the pasta, the remaining 2 tablespoons butter and the vinegar. Using tongs, toss until the sauce clings to the pasta, the pasta is heated through and the butter is melted, adding more cooking water if needed so the noodles are lightly sauced.

Step 4

Off heat, toss in the Parmesan, then taste and season with salt and pepper. Serve sprinkled with additional Parmesan.