Penne with Crisp Prosciutto, Zucchini and Corn

Bring a large pot of well-salted water to a boil. Meanwhile, put 2 tablespoons oil and the prosciutto in a large skillet, place over medium heat, and cook, stirring occasionally, until the prosciutto browns in places and becomes crisp, about 5 minutes. Transfer the prosciutto to a large plate lined with paper towels.
Add 1 tablespoon oil and the onion to the skillet, sprinkle with 1/2 tsp. salt, and cook, stirring occasionally, until the onion softens completely and turns light brown, about 6 minutes; add 1 or 2 tablespoons water to the skillet if the onion starts to stick or burn. Add the zucchini and corn, sprinkle with 1/4 tsp. salt, and cook, tossing occasionally, until the zucchini becomes tender, 4 to 5 minutes. Remove from the heat and stir in half the cheese and all the mint.
Add the penne to the pot of boiling water and cook according to the package directions. Reserve 1/2 cup of the pasta water and then drain the pasta. Add the pasta, the remaining 2 tablespoons oil, the vinegar, and 1 teaspoon black pepper to the skillet with the zucchini and corn mixture. Set the skillet over medium heat and cook, stirring, for 1 minute so the pasta mixes with the vegetables. Add the reserved pasta water and stir. Serve sprinkled with the crisp prosciutto and the remaining cheese.