Preheat the oven to 350°F (175°C).
In a small bowl, beat the eggs, reserving 2 tablespoons for brushing the crescent rolls later.
Heat a skillet over medium heat and scramble the remaining eggs until fluffy. Remove from heat and set aside.
Unroll the crescent roll dough on a flat surface and separate it into 8 triangles.
Cut each cheddar cheese slice in half and place one half on the wide end of each crescent triangle.
Spoon a portion of scrambled eggs and place one sausage link on top of the cheese.
Roll up the dough loosely, starting from the wide end and tucking in the filling.
Arrange the roll-ups on an ungreased cookie sheet.
Brush the tops with the reserved beaten egg, then sprinkle with salt and pepper.
Bake in the preheated oven for 15–18 minutes, or until the rolls are golden brown and cooked through.
Let cool slightly before serving.