Prepare selected vegetable. Bring 2 quarts of water to boil in a large kettle. Add salt and pasta to the boiling water. Using package cooking times as a guide, cook the pasta, partially covered and stirring frequently, until al dente.
Meanwhile, in a large skillet, heat fat and garlic over medium-high heat until the garlic just starts to sizzle. If using onion, heat the fat, add the onion and saute until soft, 3 to 4 minutes. Add the prepared vegetable to the pan, sprinkling generously with salt and pepper; saute until tender, 5 to 7 minutes longer. Stir in optional flavorings and dried herbs; cook to blend flavors, about 1 minute longer. Remove from heat and set aside, uncovered, until the pasta is done.
Drain the pasta, reserving 1/2 cup of the cooking liquid. Return pasta to the pot; add the contents of the skillet, pasta cooking liquid, optional fresh herbs, and a generous sprinkling of Parmesan cheese; toss to coat. Taste, adjust seasonings, including pepper to taste. Serve with additional cheese passed separately.