Remove the crescent roll dough from the container and roll into a ball. Let it sit for 15 minutes so the dough is easier to use. Preheat the oven to 375 degrees and line a baking sheet with a silpat mat.
Add the butter to a skillet over medium heat, add the mushrooms then cook, stirring occasional for 3-4 minutes. Add the ham and cook, for 1 minute; remove from the skillet and set aside. Coat the same skillet with cooking spray over medium heat. Whisk the eggs together with the milk, sea salt, freshly cracked pepper, and cayenne pepper, to taste. Pour the egg mixture into the skillet. Constantly fold the egg mixture from the bottom of the pan to the top. This will keep it from overcooking and the middle section will stay soft and fluffy. Do this constantly for 1 or 2 minutes, or until the eggs are just set. Don't overcook - they will finish cooking in the oven. Remove from the heat then add the mushroom and ham mixture as well as the green onions to the eggs and gently mix until combined.
Roll (or spread) the dough out on top of the silpat mat into a rectangle. Place the egg down the center of the dough. Add the scrambled egg mixture then the cheese on top. Cut even slits on both sides of the filling with a pizza cutter. Fold the ends over the filling then starting at one end, fold alternating strips at an angle across the filling.
Place into the oven and bake for 13-15 minutes. Remove from the oven and let it rest for 1-2 two minutes before slicing and serving. Enjoy.