In a medium skillet over medium-high heat, cook the sausage, breaking it up with a spoon or spatula, until browned and cooked through (5-7 minutes). Drain excess grease and set aside.

In a medium bowl, whisk together eggs, milk, salt, and pepper until combined.

Melt butter in the same skillet over medium heat. Pour in egg mixture and cook, stirring gently, until softly scrambled and just set.

Slice croissants in half horizontally. Warm slightly in toaster oven, oven, or microwave.

Place croissant bottoms on plates. Top with sausage and scrambled eggs.

Place cheese slice on top of eggs. Cover with croissant tops. Melt cheese in warm oven or toaster oven if needed.