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, swirling to coat the surface evenly.
03 - Pour the egg mixture into the heated 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 across the surface, followed by the diced tomato. Cover the skillet and cook for 2 to 3 minutes until the cheese starts melting.
05 - Scatter the diced avocado and optional chives or green onions over one half of the omelette. Using a spatula, gently fold the opposing half over the filling.
06 - Cook the folded omelette for 1 additional minute, allowing the cheese to fully melt and the avocado to warm through. Slide onto a plate, slice in half, and serve immediately.