Crack the eggs into a mixing bowl and add the milk, salt, and black pepper. Whisk until well combined and slightly frothy.

Heat a non-stick skillet over medium-low heat and add the butter. Let it melt and coat the pan.

Pour the egg mixture into the skillet. Let it sit undisturbed until it begins to set around the edges.

Gently stir the eggs using a spatula, pushing from the edges to the center. Continue cooking and stirring until mostly set but slightly runny.

Sprinkle cheddar cheese over the eggs and gently fold to incorporate. Cook another minute until cheese melts and eggs are fully cooked but soft.

Remove from heat and serve immediately on a warm plate.