01 - In a medium bowl, whisk together the eggs, milk or cream, salt, and black pepper until slightly frothy and well combined.
02 - Melt the butter in a non-stick skillet over medium heat, tilting the pan to coat the surface evenly.
03 - Pour the egg mixture into the skillet and swirl to cover the base evenly. Cook undisturbed for about 2 minutes until the edges begin to set.
04 - Sprinkle the shredded cheese evenly over one half of the omelette. Arrange the diced tomato and avocado over the cheese.
05 - When the eggs are almost fully set but still slightly runny on top, gently fold the omelette in half using a spatula, enclosing the filling.
06 - Continue cooking for 1 to 2 minutes until the cheese has fully melted and the omelette is cooked through while remaining creamy inside.
07 - Slide the omelette onto a plate, garnish with chopped chives or green onions if desired, and serve immediately.