Crack the eggs into a bowl. Add the milk, salt, and black pepper, then whisk just until the yolks and whites are blended.

Melt the butter in a nonstick skillet over low to medium-low heat, tilting the pan to coat it.

Pour in the egg mixture and let it sit for a few seconds, until a thin layer starts to set around the edges.

Gently push the eggs from the edges toward the center with a spatula, making soft folds. Continue slowly as uncooked egg flows into the open spaces.

When the eggs are mostly set but still glossy, remove the skillet from the heat. Fold in chives if using and serve immediately.