First, peel the potatoes and cut them into thin sticks. Rinse them in water up to 3 times until the water runs clear. Heat about 1/2 inch of olive oil in a skillet. When the potatoes are soft, remove them from the oil and drain on paper towels. Sprinkle with a pinch of salt.

Beat the eggs in a large bowl, add the potatoes, and mix well. Let the mixture rest for 10 minutes to help the omelette set.

To make the caramelized onions: slice the onions thinly and cook them in a skillet with olive oil over low heat, stirring occasionally. Let them cook slowly until they become soft and sweet. The longer they cook, the sweeter they will be. Set aside.

Continue with the omelette: pour a layer of the potato and egg mixture into a skillet over medium heat. Add the caramelized onions on top of this first layer, spreading them evenly, then cover with the remaining potato and egg mixture.

Gently shake the skillet and check if the bottom has set. When it has, carefully flip the omelette using a plate to cover the skillet, then slide it back in to cook the other side.

After a few seconds, your omelette will be ready. At this point, you can cook it to your preferred doneness. Remove from the skillet when it's as set as you like. Serve with some good homemade bread and enjoy!