Preheat the oven to 375 degrees. Line a baking sheet with parchment paper.
Make the scrambled eggs by melting the butter in a large nonstick skillet over medium heat. Add the very well whisked eggs into the skillet then season with sea salt and freshly cracked pepper, to taste.
Wait for the edges to just barely start to set, then using a rubber spatula, gently push the eggs from one end of the pan to the other. Continue this process, pausing in between swipes to allow the uncooked egg to settle on the skillet and cook, gently pushing the liquid to cook and form into fluffy curds. Remove from the heat when the eggs are softly scrambled; set aside until needed. Side Note: Don't overcook the eggs because they will continue cooking in the oven.
Make the roll ups by unrolling the crescent dough and place on the baking sheet.
Place one slice of cheese down the center of the wide end of each dough triangle. Next, divide the scrambled eggs evenly on top of the cheese slices, then add one sausage link on top of the eggs.
Starting at the wide end, roll up crescent dough and place seam side down, making sure to tuck in any loose corners.
Bake the sausage and egg roll ups in the oven until golden brown, about 13-15 minutes.