Crack the eggs into a bowl and add milk, salt, and pepper.
Whisk the mixture until fully combined and frothy.
Heat a non-stick skillet over medium heat and add butter.
Pour in the egg mixture and let it cook undisturbed for about 1 minute.
Gently lift the edges to allow uncooked eggs to flow underneath.
Add cheese and vegetables on one half when mostly set.
Fold the omelette in half over the filling.
Cook for another minute until the cheese is melted.
Slide the omelette onto a plate and serve hot.