In a bowl, crack the eggs and add milk, salt, and pepper. Beat until well combined and slightly frothy.
Place the non-stick skillet over medium-low heat and add butter. Melt completely, coating the pan.
Pour the egg mixture into the skillet. Let it sit until it starts to set around the edges.
Gently stir the eggs, pushing them from the edges toward the center. Continue until mostly cooked.
When the eggs are slightly runny, sprinkle cheese on top and let it melt.
Remove from heat when eggs are still soft; they will continue cooking from residual heat.
Transfer eggs to a plate, garnish with chives, and enjoy immediately!
