Preheat oven to 375°F (190°C).
In a bowl, whisk together eggs, milk, salt, and pepper.
Melt butter in a skillet over medium heat.
Add egg mixture and scramble until just set; remove from heat.
Unroll crescent roll dough and separate into 6 triangles.
On each triangle, place one cooked sausage link.
Top each sausage with a spoonful of scrambled eggs and some shredded cheddar cheese.
Roll up each crescent triangle starting at the wide end, wrapping around the sausage and filling.
Place roll-ups on a baking sheet lined with parchment paper, seam side down.
Bake for 15-20 minutes or until golden brown and puffed.
Remove from oven and let cool slightly before serving.