Sauté the onion over a medium heat in the oil until tender, approximately 5 minutes.
Add the garlic and mushrooms, season with salt and pepper, and and cook over a high heat until the mushrooms are done.
Add the white wine and allow it to reduce to at least half.
Add the zucchini bits and a splash of the chicken broth.
Once the broth has reduced to nothing, add a little bit more until the zucchini is cooked to your desired level. You might not use the whole cup of broth.
Once the zucchini is cooked, remove from the heat, and add the cream, butter, and parmesan cheese.
Stir until the cheese is melted.
Garnish with freshly chopped parsley and serve immediately.