Crack the eggs into a bowl and add milk, salt, and pepper. Whisk until well combined.
Heat a non-stick skillet over medium heat and add butter.
Pour the egg mixture into the skillet, tilting to spread evenly.
Cook for 1-2 minutes until the edges start to set.
Add chopped vegetables evenly over half the omelet.
Sprinkle cheese on top of the vegetables.
Carefully fold the omelet in half using a spatula.
Cook for an additional minute or until the cheese melts.
Serve hot and enjoy!