01 - Crack the eggs into a mixing bowl. Add the milk, salt, and pepper. 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 skillet and cook undisturbed for about 2 minutes, until the edges begin to set.
04 - Sprinkle the shredded cheese evenly over the eggs, followed by the diced tomato. Cover the skillet and cook for another 2 to 3 minutes until the cheese starts to melt.
05 - Scatter the diced avocado and chives or green onions, if using, over one half of the omelette. Using a spatula, gently fold the opposite half over the filling.
06 - Cook for 1 more minute, allowing the cheese to finish melting and the avocado to warm through. Slide onto a plate, slice in half, and serve immediately.