Whisk the eggs, milk, salt, and pepper in a bowl until the yolks and whites are completely blended and a little frothy.
Melt the butter in a nonstick skillet over low heat.
Pour in the eggs. Stir slowly and constantly with a heatproof spatula, sweeping the pan as soft curds form, about 2 minutes.
Take the pan off the heat while the eggs still look shiny and slightly loose. Cover and let them rest 1–3 minutes — they finish cooking in the warmth of the pan.
Serve right away.
The eggs are done before they look done. Left in the hot pan, they turn rubbery and start to weep liquid.