Step 1

On the large holes of a box grater, grate each onion half, holding each piece by the root end; discard the ends. Then shred the carrot, mushroom and celery. In a large saucepan over medium, combine the oil, grated vegetables and 1 teaspoon salt. Cook, stirring, until gently sizzling, then reduce to medium-low, cover and cook, stirring occasionally, until meltingly tender and any moisture released has cooked off but the vegetables have not browned, about 20 minutes.

Step 2

Meanwhile, in a large pot, boil 4 quarts water. Stir in the pasta and 1 tablespoon salt, then cook, stirring occasionally, until al dente. Reserve about 1½ cups of the cooking water, then drain the pasta and return it to the pot.

Step 3

When the vegetables are done, add the wine and cook over medium, uncovered and stirring occasionally, until almost completely evaporated, 3 to 5 minutes. Add the tomato paste and ½ teaspoon pepper; cook, stirring, until the mixture starts to brown and stick to the bottom of the pan, 3 to 5 minutes.

Step 4

Stir 1 cup of the reserved pasta water into the sauce mixture, then add the sauce to the pasta in the pot. Cook over medium, tossing with tongs, until the sauce coats the noodles, about 3 minutes, adding more pasta water 1 tablespoon at time as needed if the mixture is dry. Taste and season with salt and pepper. Serve drizzled with additional oil.

Step 5

Optional garnish: Finely grated pecorino Romano or Parmesan cheese OR chopped fresh basil OR flat-leaf parsley OR both