This is great for breakfast, brunch or lunch.
1. Pour 2 tablespoons of the olive oil into a 12-inch non-stick skillet over medium heat and add 1/2 teaspoon of the salt. Carefully add the onions and cook until golden, stirring occasionally, about 20 minutes. Transfer the onions to a bowl and allow them to cool, but set the pan aside because you’ll reuse it shortly. While the onions are cooking, peel the potatoes and cut them into 1/2-inch cubes or half-moon-shaped slices. In a saucepan of boiling salted water, cook the potatoes until almost tender, about 8 minutes. Drain in a colander and allow them to cool there. When the potatoes have cooled, combine the onions and potatoes. (The onion and potato mixture may be made 1 day ahead and chilled, covered.)
2. In a large bowl whisk together the eggs, scallions, rosemary, remaining 1/2 teaspoon salt and the pepper. (I add a lot of black pepper to this omelette but start with a little and see what you prefer.) Add the cooked onion-potato mixture and stir to combine.
3. In the same non-stick skillet used to sauté the onions, heat the remaining 3 tablespoons of oil over medium-high heat until hot but not smoking. Add the egg mixture, spreading potatoes evenly across the pan. Reduce the heat to medium and gently stir eggs for about 1 minute or until the omelette begins to set. Shift the skillet so that one quarter of the omelette is directly over the center of the burner and cook for 1 minute. Shift skillet three more times, cooking each skillet quarter for 1 minute. Reduce the heat to low, center the skillet over the burner, and continue to cook the omelette until almost set, about 4 minutes.
4. Slide the omelette, bottom side down, onto a baking sheet or a large heatproof platter, and then invert the omelet back into skillet. Cook the other side of the omelette over low heat until golden, about 4 minutes. Slide the omelette onto a platter and allow to cool before serving. Garnish with chopped scallion and parsley if you like.
5. If made ahead and refrigerated, allow the omelette to come to room temperature before serving. This may be served warm or at room temperature.