Whisk the eggs, salt, pepper, and milk together until light and foamy. Add the butter to a 10- to 12-inch carbon steel skillet and put over high heat.
When the butter bubbles, after about 1 minute, pour the eggs straight into the middle of the pan, which will force the butter to the edges, where it's needed. Stir slowly with a rubber or silicone spatula.
As soon as curds (big soft lumps) of eggs begin to form, drop the heat to low and shift from stirring to folding the curds over on themselves while gently shaking the pan with the other hand. As soon as no more liquidous egg is running around the pan, kill the heat and gently transfer the scramble to a warmed plate. Let the eggs rest for 1 minute before serving.