Preheat your oven to 375°F (190°C). Prepare a baking sheet by lining it with parchment paper to prevent sticking.
In a medium mixing bowl, vigorously whisk together the eggs and milk. Season with salt and black pepper, and continue whisking until the mixture is well combined. Gently fold in the shredded cheddar cheese and the chopped chives or green onions, making sure they are evenly distributed.
In a skillet over medium heat, cook the breakfast sausages until they are nicely browned and cooked through, about 8-10 minutes. Make sure to rotate them for even cooking. Once done, remove the sausages from the skillet and allow them to cool slightly on a plate.
On a clean, flat surface, unroll the crescent roll dough. Carefully separate the dough into the pre-scored individual triangles.
Take one sausage and place it at the wide end of each dough triangle. Roll the dough around the sausage, starting from the wide end and working towards the tip, making sure to fully enclose the sausage within the dough.
Arrange the rolled sausages on the prepared baking sheet, ensuring there is enough space between each one for even baking.
Using a spoon, drizzle the egg and cheese mixture generously over the top of each rolled sausage, allowing some of the egg mixture to soak into the crescent dough for extra flavor.
Place the baking sheet in the preheated oven and bake for 12-15 minutes, or until the crescent dough turns a beautiful golden brown and feels cooked through.
Once baked, remove the pan from the oven and allow the breakfast pigs in a blanket to cool for a few minutes before serving.