Prepare a pot of water for the pasta. Add about 1 tablespoon of salt, bring the water to a boil.
Melt the butter in a large saute pan and add the garlic, zucchini, and ham. Stir and cook for about a minute then add the tomatoes and mushrooms and cook for another 2-3 minutes.
Add the broth, stir gently to combine and bring the mixture to a boil. Add the cream, stir to combine, then reduce the heat so the mixture is just simmering.
Stir in the Parmesan cheese. Reduce the heat and keep the mixture warm.
Cook the pasta according to the package directions, usually about 2-3 minutes. Drain the pasta and add it to the pan and toss the mixture gently with tongs to distribute the sauce and vegetables evenly. Top the pasta with the basil and serve immediately.
Notes: A small amount of fried pancetta could be used in place of the ham, or even tiny slices of prosciutto.