Remove the ends of the zucchini and, if they are large, cut in half lengthwise. Slice the zucchini diagonally in 1/2-inch slices. Heat 2 tablespoons of olive oil in a large (12-inch) saute pan and add the onions. Cook for 10 minutes on medium-low heat, until they start to brown.
Add half the zucchini, 1 teaspoon salt, and 1/4 teaspoon pepper to the pan and cook, tossing occasionally, for 10 to 15 minutes, until just cooked through. Sprinkle with Parmesan and cook for 30 seconds more. Remove to a serving platter and repeat with the rest of the zucchini. Serve immediately.
Note: If you cook too much zucchini in one pan, you end up steaming rather than sauteing it. We prefer to cook it in 2 batches.