Heat oil over medium-high heat in a large skillet. Add potatoes and season lightly with salt and pepper; cook, stirring occasionally, until golden brown and crisp, 10 to 14 minutes. Add onions; cook and stir until soft and beginning to brown, 6 to 8 minutes.

Whisk eggs in a bowl; season with salt and pepper. Pour eggs into the skillet and stir gently to combine with potatoes and onion. Reduce the heat to low and cook until eggs begin to brown on the bottom, 4 to 5 minutes.

Loosen omelette with a spatula. Invert a large plate over the pan, and carefully flip omelette out onto the plate. Slide omelette, uncooked-side down, back into the pan. Cook until eggs are set, 4 to 5 minutes.