Wash the asparagus under cold water. Remove the tough bottoms sections of the spears and discard. Cut off the tips and set aside. Cut the remaining sections into large pieces. Steam (or boil) the chopped portions for about 5 minutes or until tender. Remove from heat, and set aside (apart from the tips).
Heat the oil in a large skillet over medium heat, and add the onion. When translucent add the steamed asparagus. Cover and cook together for about 5 minutes. Add salt and pepper to taste. Remove to a food processor and blend until pureed.
In the same skillet, add the asparagus tips and a few tablespoons of water. Cover and cook for a couple of minutes. Add back the pureed asparagus and cover. Cook for a few minutes, ensuring that the tips are tender and the sauce is hot.
Bring a large pot of salted water to a boil. Cook the pasta until al dente, drain it, retaining some of the cooking water. Add the pasta to the skillet with the asparagus and mix thoroughly. Add some of the retained cooking water if it seems dry.
Serve immediately with a sprinkle of Parmigiano.
O’ Vesuvio is a special shaped pasta from Campania. In dialect, the o’ means “the.” Vesuvio is Mount Vesuvius.