In a large skillet, heat the fully cooked breakfast sausage links over medium heat for about 5-7 minutes, turning them occasionally until browned and heated through. Chop into bite-sized pieces.

In the same skillet, lower the heat to medium-low and add 1 tablespoon of butter. Whisk together the eggs and milk until combined, then pour into the skillet. Gently scramble for about 3-5 minutes until just set.

Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper. Roll out the crescent dough, pinch the seams to seal. Add scrambled eggs, sausage pieces, and cheddar cheese to each triangle of dough and roll up each triangle tightly.

Arrange the roll-ups on the baking sheet, bake for 12-15 minutes until golden brown and cheese is melted.