01 - Crack the eggs into a mixing bowl. Add the milk, season with salt and pepper, and whisk vigorously until fully blended and slightly frothy.
02 - Melt the butter or heat the olive oil 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 let it cook undisturbed for about 2 minutes, until the edges begin to set while the center remains slightly loose.
04 - Scatter the shredded cheese evenly across the surface of the eggs, then distribute the diced tomato over the cheese. Cover the skillet and cook for 2 to 3 minutes until the cheese starts to melt.
05 - Arrange the diced avocado and chopped chives or green onions, if using, over one half of the omelette.
06 - Slide a spatula beneath the unfilled half and gently fold it over the avocado side. Cook for 1 additional minute to allow the cheese to melt completely and the avocado to warm through.
07 - Transfer the omelette to a plate, cut it in half, and serve immediately while hot.