How to Make It
Preheat the oven to 500°. Warm 1/4 cup of the oil in a 12-inch nonstick ovenproof skillet over moderately high heat. Add the potatoes, cover and cook over low heat until browned on the bottom and tender, about 15 minutes. Add the onion, season with salt and pepper and cook, stirring, until the onion is softened but not browned, about 3 minutes.
Increase the heat to moderate and drizzle the remaining 1 tablespoon of oil around the edge of the skillet. In a large bowl, whisk the eggs with a large pinch of salt and a small pinch of pepper. Pour the eggs into the skillet. As the eggs cook, use a spatula to draw them into the center, allowing the runny egg to fill the bottom of the skillet. Continue cooking and drawing the cooked egg into the center until the eggs are almost set, about 4 minutes.
Transfer the skillet to the oven and bake the omelet for 5 minutes, or until just firm and lightly browned on top. Slide the omelet onto a cutting board and let cool to room temperature. Sprinkle the parsley over the omelet, cut into 6 wedges and serve.