In a large skillet over medium heat, cook the breakfast sausage links for about 8–10 minutes, until browned and heated through. Transfer to a paper towel-lined plate to drain excess grease.

In a medium bowl, whisk together eggs, milk, salt, and pepper until well combined. Melt butter in the skillet, then pour in the egg mixture and scramble for 3–5 minutes until just set.

Preheat oven to 375°F. Unroll crescent roll dough and separate into triangles. Place cooked sausage, scrambled eggs, and cheddar cheese in the center of each triangle, then fold edges to create roll-ups.

Arrange roll-ups on a lined baking sheet and bake for 12–15 minutes until golden brown and flaky.