1. Wash the zucchini and grate it with a large grater or slice it into very thin rounds.
2. Finely slice the onion or shallot.
3. Heat the oil in a skillet.
Add the onion and zucchini, lightly salt, and sauté over medium heat for 5 to 7 minutes.
4. Beat the eggs in a bowl with the milk, salt, and pepper.
5. Pour the egg mixture over the vegetables in the skillet.
6. Cook over low heat until the omelette is set on the edges, but still slightly runny in the center.
7. Fold the omelette in half, let it rest for a minute off the heat.
8. Serve hot or cold according to preference.