Heat the olive oil in a large skillet over medium heat.
Add the shallots and garlic, and saute until wilted and limp.
Add the mushrooms and saute for 2 minutes, then add the zucchini. Cook until the zucchini softens, about 4 minutes.
Add the basil chiffonade and white wine, and cook until the wine reduces by about one half. Add the grated Parmesan and cook for 2 more minutes. Toss with the cooked pasta.