Prepare the Eggs: In a bowl, whisk the eggs with milk, salt, and pepper until well combined.
Cook the Bacon: In a non-stick skillet, cook the chopped bacon over medium heat until crispy. Remove and set aside, leaving some grease in the pan.
Make the Omelet: In the same skillet, add butter and let it melt. Pour the egg mixture into the pan, tilting it to spread evenly. Allow it to cook undisturbed for about 2-3 minutes or until the edges start to set.
Add Fillings: Once the omelet is mostly cooked, sprinkle the bacon and cheese over one half. Fold the omelet in half and cook for another minute or until the cheese is melted.
Serve: Slide the omelet onto a plate and garnish with chopped chives or parsley if desired. Enjoy warm!