Heat oven to 450° F. In a bowl, toss the zucchini with 2 tablespoons of the oil and set aside.
On a lightly floured surface, roll out the dough in the shape of a rectangle, to a thickness of ⅛ to ¼ inch. Transfer to a lightly greased baking sheet.
Top the dough with the zucchini, overlapping slightly and leaving a 1-inch border. Sprinkle with ¼ teaspoon salt.
Bake until the crust is a light golden brown, 20 to 25 minutes.
Meanwhile, heat the remaining oil in a skillet over medium heat. Add the mushrooms, onion, and ¼ teaspoon salt. Cook until lightly golden, 4 to 5 minutes.
Cut the pizza and serve topped with the mushroom-onion mixture and Parmesan.