Preheat grill to high. Whisk eggs and milk in a medium bowl. Season with salt and pepper.
Heat 2 tsp oil in a non-stick 20cm frying pan. Pour in egg mixture and cook over medium heat for 3-4 minutes until almost set. Sprinkle omelette with cheese and place under hot grill for a few minutes until puffed and golden.
Toss avocado and tomato with lemon juice and remaining teaspoon of oil. Sprinkle avocado mixture and half the herbs over one-half of omelette. Fold omelette in half and slide onto a warm plate to serve. Scatter with remaining herbs.