Bring a large pot of water to a boil. Add potatoes and boil for 5 minutes. Drain and set aside.

Heat olive oil in a deep cast iron skillet over medium heat. Add zucchini and onion; saute until golden, 5 to 7 minutes. Add drained potatoes and stir gently to incorporate.

Beat eggs in a bowl with oregano, cayenne pepper, salt, and pepper. Pour egg mixture into the skillet until evenly distributed; stir gently with a fork. Cook until eggs are set, 5 to 10 minutes.