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 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 2 to 3 minutes until the cheese begins to melt.
05 - Arrange the diced avocado and chives or green onions (if using) over one half of the omelette.
06 - Using a spatula, gently fold the uncovered half of the omelette over the filling. 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 in half, and serve immediately.