In a large bowl, whisk together the eggs, milk, salt, and pepper until well combined and slightly frothy.
Melt the butter in a large non-stick skillet over medium-low heat. Make sure the butter coats the entire bottom of the pan.
Pour in the egg mixture and let it sit undisturbed for about 20 seconds. Using a rubber spatula, gently push the eggs from the edges toward the center, allowing the uncooked eggs to flow to the edges.
Continue this process for 3-4 minutes until the eggs are mostly set but still slightly wet. If using cheese, sprinkle it on now.
Remove from heat immediately (the eggs will continue cooking from residual heat). Garnish with fresh chives if desired and serve alongside buttered toast for the perfect warm breakfast plate.