Peel and finely chop the onion. Put it with the butter in a 10-inch skillet. Place over medium-high heat and sauté, stirring occasionally, until it 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, unravel the pancetta and cut into thin strips about 1 inch long. When the onion is done, add the pancetta and cook until it begins to brown, 2 to 3 minutes. Add the peas, season with salt and pepper, and stir until well coated. If using fresh peas, add just enough water to cover the peas. Lower the heat to medium and cook, uncovered, until the peas are tender, about 20 minutes if using fresh or 10 minutes if using frozen. If the pan dries out before the peas are tender, add a little water. When the peas are done, there should not be any liquid left in the pan.
Add about 2tablespoons salt to the boiling water, put in the pasta, and stir well. Cook until al dente.
Add the cream to the peas and cook until the cream is thick enough to coat a spoon, 1 to 2 minutes. Remove from the heat.
When the pasta is done, drain it well, toss with the sauce and the Parmigiano, and serve at once.