Heat olive oil in a large non-stick skillet over medium heat.
Add sliced potatoes and onion, season lightly with salt and pepper.
Cook gently for 15–20 minutes, stirring occasionally, until potatoes are soft but not crispy.
Drain excess oil from the potatoes and onions and reserve it for cooking.
Crack eggs into a large bowl, add a pinch of salt and pepper, and beat lightly until combined.
Add the cooked potatoes and onions to the beaten eggs and mix gently.
Let the mixture rest for 5 minutes to absorb flavor.
Return about 1 tablespoon of reserved oil to the skillet and heat over medium.
Pour in the egg and potato mixture, spreading evenly, and cook for 5–7 minutes until the bottom is golden and mostly set.
Place a large plate over the skillet and carefully invert the pan to flip the omelette onto the plate.
Slide the omelette back into the skillet to cook the other side for 4–5 minutes until set but slightly soft in the center.
Transfer the omelette to a serving plate and let it rest for 5–10 minutes before slicing.
Serve warm or at room temperature.