Heat the butter in a skillet over medium-low heat.
Whisk the eggs and milk in a medium bowl until just incorporated. Do not over beat.
When the butter is melted and foamy (tiny bubbles will form and pop), add in the egg mixture.
Let the egg set for about 10-15 seconds (the edges should become thin and slightly crispy, but the middle should still be liquid)
With a spatula, begin from the outer edge and bring to the middle a streak of egg. Repeat around the circumference of the skillet until all the egg is in the middle. The egg should still be slightly underdone. Use the spatula to break up any wide ribbons.
When the eggs are mostly cooked (some spots of glistening egg batter), off the heat, remove eggs from the pan and serve.