Following the directions on package, cook the ziti in a large pot of salted boiling water. 2 minutes before the ziti is done, add chopped asparagus to the pasta and water. When ziti is done, drain, reserving 1 cup of pasta water.
Heat the oil in a heavy large skillet over medium heat. Add the garlic and saute until fragrant, about 20 seconds.
Add asparagus and pasta to the skillet. If needed, add some of the reserved cooking liquid. (I used almost all of it.) Toss to coat.
Add the prosciutto, mozzarella, and basil, and toss to combine. Turn off the heat. Season with salt and pepper, to taste, and serve.