01 - Crack the eggs into a mixing bowl, add the milk, season with salt and pepper, and whisk vigorously until well combined and slightly frothy.
02 - Melt the butter or heat the olive oil in a non-stick skillet over medium heat, tilting to coat the surface evenly.
03 - Pour the egg mixture into the skillet and cook undisturbed for about 2 minutes, until the edges begin to set while the center remains slightly loose.
04 - Sprinkle the shredded cheese evenly over the surface, then scatter the diced tomato on top. 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 - Gently slide a spatula under the unfilled half and fold it over the avocado side. Cook for 1 more minute to finish melting the cheese and warm the avocado through.
07 - Slide the omelette onto a plate, cut it in half, and serve immediately while warm.