01 - In a medium bowl, whisk together the eggs, milk or cream, salt, and black pepper until slightly frothy.
02 - Heat butter in a non-stick skillet over medium heat until melted and lightly bubbling.
03 - Pour the egg mixture into the skillet and swirl to cover the base evenly. Cook undisturbed for about 2 minutes, until the edges start to set.
04 - Sprinkle cheese evenly over half of the omelette. Top with diced tomato and avocado.
05 - When the eggs are almost fully set but still slightly runny on top, gently fold the omelette in half over the filling.
06 - Cook for an additional 1 to 2 minutes until the cheese has melted and the omelette is cooked through but still creamy inside.
07 - Slide onto a plate, garnish with chopped chives or green onions if desired, and serve immediately.