Preheat oven to 450º 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 1/8 to 1/4 inch, and transfer to a lightly greased baking sheet. Top the dough with the zucchini, overlapping slightly and leaving a 1-inch border around the edge. Sprinkle with half the salt. Bake until the crust is a light golden brown, 20 to 25 minutes.
Meanwhile, heat the remaining oil in a small skillet over medium heat. Add the mushrooms, onion, and remaining salt and cook until lightly golden, 4 to 5 minutes. Set aside.
Cut the pizza and serve it topped with the mushrooms and onion, and Parmesan.