Stir the eggs and Parmesan cheese together in a bowl; set aside.
Heat the olive oil in a large frypan over medium-high heat; cook the zucchini in the hot oil until softened and lightly browned, about 7 minutes. Season the zucchini with garlic powder, salt, and pepper. Reduce heat to medium; pour the egg mixture into the frypan. Cook, stirring gently, for about 3 minutes. Remove the frypan from the heat and cover. Keep covered off the heat until the eggs set, about 2 minutes more.