If using fresh peas, shell them. Peel and finely chop the onion. peel the tomatoes and coarsely chop.
Put the butter and onion in a 10-inch skillet and place over medium heat. Sauté, stirring occasionally, until the onion turns a rich golden color, about 5 minutes.
Fill a pot for the pasta with at least 6quarts water, place over high heat, and bring to a boil.
While the onion is sautéing, remove the casing from the sausage if using links. When the onion is done, add the sausage and break it up with a spoon. Sauté until the sausage is nicely browned, 3 to 4 minutes. Add the tomatoes and peas. If using fresh peas, cover the pan and cook, covered, over medium heat for 15 minutes. If using frozen peas, proceed to the next step.
Season with salt and pepper and cook, uncovered, until the tomatoes are reduced and no longer watery, about 15 minutes. Set aside.
Add about 2tablespoons salt to the boiling water, put in the pasta, and stir well. Cook until al dente. When the pasta is done, drain it well, toss with the sauce and Parmigiano, and serve at once.