In a saucepan combine potato with water and cover. Bring to a boil and cook until potato is tender, about 20 minutes. Drain and cool.
In a large bowl, whisk eggs until well beat. Whisk in water and salt and set aside.
Preheat broiler. Peel the cooled potato and cut into bite-sized cubes. Set aside.
In a large ovenproof frying pan, warm two tbsp. of olive oil over medium heat. Add the onion and cook until softened. Add the garlic and rosemary and cook another two minutes.
Evenly spread out the potato in the pan over medium heat. Add the remaining two tbsp. of oil and butter and swirl the pan until the butter melts. Pour the egg mixture, season with pepper, reduce heat to low, and cook slowly until the sides and bottom are set but the center is still loose, about four minutes. Run a spatula along the sides of the pan to keep from sticking.
Transfer the pan to the broiler and broil until the top sets and browns slightly, about two minutes. Cut into wedges and serve warm.