Preheat your oven to 375°F (190°C) and prepare a baking sheet by lining it with parchment paper or lightly greasing it with butter or cooking spray.
Open the can of crescent roll dough and carefully unroll it on a clean surface. Separate the dough into individual triangles as indicated on the packaging.
In a small bowl, combine the milk, salt, and black pepper. This mixture can be brushed onto the dough for added flavor if desired.
Place a sausage link at the wide end of each triangle of dough. Sprinkle a small amount of shredded cheddar cheese over the sausage.
Starting from the wide end, roll the dough around the sausage and cheese, ensuring it is tightly wrapped. Pinch the edges to seal the dough and prevent any filling from escaping during baking.
Arrange the rolled pigs in a blanket on the prepared baking sheet, leaving space between each one to allow for expansion.
Bake in the preheated oven for 12 to 15 minutes or until the dough is golden brown and cooked through.
Remove from the oven and let cool for a few minutes before serving. Enjoy your breakfast pigs in a blanket warm!