Step 1: Prepare the Eggs : Crack eggs into a medium bowl. Add milk, salt, and pepper. Whisk until smooth and slightly frothy.
Step 2: Heat the Pan : Heat a non-stick skillet over medium-low heat. Add butter and allow it to melt, coating the pan evenly.
Step 3: Cook the Eggs : Pour the egg mixture into the skillet and let it set for 1–2 minutes without stirring. Gently lift the edges with a spatula, tilting the pan to let uncooked eggs flow underneath.
Step 4: Add Ham, Cheese, and Chives : When eggs are mostly set but still slightly creamy, add diced ham, shredded cheese, and chopped chives on one half of the omelette. Fold the omelette over the filling and cook for another 1–2 minutes until the cheese melts and eggs are fully set.
Step 5: Serve : Slide the omelette onto a plate. Garnish with extra chives if desired and serve hot.