Instructions

1. In a non-stick skillet, heat 1 tablespoon of the unsalted butter over medium heat until melted.
2. Add the sliced onion to the skillet. Stir occasionally, cooking until the onions are caramelized and golden brown, about 15 minutes. Remove from heat and set aside.
3. In a mixing bowl, whisk together the eggs, milk, salt, and black pepper until well combined and slightly frothy.
4. In the same skillet, add the remaining tablespoon of butter and let it melt over medium heat.
5. Pour the egg mixture into the skillet, allowing it to spread evenly. Cook undisturbed for a few minutes until the edges begin to set.
6. Using a spatula, gently lift the edges of the omelette and tilt the skillet to allow the uncooked eggs to flow to the edges, ensuring even cooking.
7. Once the omelette is mostly set, sprinkle the caramelized onions and grated Gruyere cheese over one half of the omelette.
8. Carefully fold the other half of the omelette over the filling. Cook for an additional minute, or until the cheese melts.
9. Slide the omelette onto a plate and serve hot, garnished with fresh herbs if desired.