Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper for easy cleanup, if desired.
In a skillet over medium heat, cook the breakfast sausage links until browned and cooked through, about 8-10 minutes. Remove from heat and let cool slightly before slicing.
Unroll the crescent roll dough and separate it into triangles.
Place a slice of cooked sausage on the wide end of each crescent triangle. Sprinkle a little cheddar cheese and parsley (if using) over the sausage.
Roll the crescent dough starting at the wide end, and roll towards the point to form a crescent shape. Pinch the edges to seal them if necessary.
Place the rolled crescent rolls on the prepared baking sheet.
In a small bowl, beat the egg and brush the egg wash over the tops of the rolls for a glossy finish.
Bake in the preheated oven for 12-15 minutes or until golden brown.
Allow the rolls to cool slightly before serving. Enjoy warm!