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 the pan to coat the surface evenly.
03 - Pour the egg mixture into the heated skillet and let it cook undisturbed for about 2 minutes, until the edges begin to set and pull away slightly from the pan.
04 - Sprinkle the shredded cheese evenly across the surface of the eggs, followed by the diced tomato. Cover the skillet and cook for another 2 to 3 minutes until the cheese starts melting.
05 - Scatter the diced avocado and 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-topped side. Cook for 1 more minute, allowing the cheese to fully melt and the avocado to warm through.
07 - Slide the omelette onto a plate, slice it in half, and serve immediately while warm.