Preheat oven to 375 degrees F. Line a baking sheet with parchment paper. Beat five of the eggs in a bowl. In a nonstick skillet over medium heat, cook butter until hot; add beaten eggs. As eggs begin to set, use a spatula to pull the eggs gently across the pan, forming large soft curds. Cook while pulling, lifting and folding until eggs are thickened and visible liquid is cooked off. Remove skillet from heat. Sprinkle flour onto work surface and unroll crescent dough over the flour. Pinch seams in dough together, then flatten dough lightly with a rolling pin. Cut dough into eight rectangles. Top a rectangle with 1/8 of the cooked eggs, 1/8 of the cheese, and a sausage link; roll up the rectangle and place on baking sheet. Repeat with remaining dough, eggs, cheese, and sausage. Beat the remaining egg and brush beaten egg over each roll; season with salt and pepper. Bake for 15 minutes or until golden brown.