In a large skillet over medium heat, sauté the onion, carrot, and celery in the olive oil until the onion is translucent. Add the asparagus and cook for 5 minutes. Add the red pepper and cook for 5 more minutes.
Bring a large pot of salted water to a boil.
Add the zucchini, and about a teaspoon of salt and pepper, and cook for an additional 5-10 minutes, or until the vegetables are thoroughly cooked, but not too soft.
Cook the pasta until al dente (about 2 minutes less than package directions), drain, and retain a cup of the cooking water. Add the pasta to the vegetables and mix together. Add a bit of the cooking water if it seems too dry.
Toss in the parsley and serve, with grated Parmigiano.