In a skillet over medium heat, add the breakfast sausage links. Cook for about 6-8 minutes, turning occasionally, until they are golden brown and cooked through. Remove from skillet and allow to cool slightly before slicing into bite-sized pieces.

In a mixing bowl, whisk together the eggs, milk, salt, and pepper until well combined. Melt butter in the same skillet over medium-low heat, then add the egg mixture. Cook gently, stirring occasionally for about 3-4 minutes, until the eggs are softly scrambled.

Preheat your oven to 375°F (190°C). Unroll the refrigerated crescent roll dough and separate into triangles. Place a portion of cooked sausage, scrambled eggs, and a sprinkle of shredded cheddar cheese at the wide end of each triangle. Roll them up starting from the wide end and pinch the edges to seal.

Arrange the assembled roll-ups on a baking sheet lined with parchment paper. Bake in the preheated oven for 12-15 minutes, or until puffed and golden brown.

Let the roll-ups cool for a few minutes before serving. Enjoy warm!