Over medium-high heat, cook sausage until no longer pink, breaking it up as it cooks. Drain off excess grease.

While the sausage cooks, in a medium bowl, whisk together eggs, milk, and pepper.

Pour into the skillet with the sausage and sprinkle cheese on top.

Cook, stirring constantly, until eggs are cooked thoroughly.

Sprinkle with additional cheese to serve, if desired.