Heat 2 tablespoons olive oil in a roasting pan or large sauté pan and add 1/2 of onions. Sauté onions 10 minutes over medium-low heat, until they start to brown. Add 1/2 of the zucchini, 1 teaspoon salt, and 1/4 teaspoon pepper, tossing occasionally, 10 to 15 minutes, until just cooked through. Sprinkle with half of Parmesan and cook 30 seconds more. Remove to a serving platter and repeat with remaining zucchini. Serve immediately.