Heat the oven to 375 degrees and spray a cookie sheet with cooking spray.
Season each side of chicken with salt and pepper and melt 2 tablespoons of the butter in a skillet over medium high heat on the stove. Cook the chicken for about 10 minutes until each side is nicely browned, and set aside.
In a small bowl, mix together the mayonnaise and 1/4 cup of parmesan cheese. This will serve as a wonderful coating for the chicken to give it an extra kick of flavor.
Unroll each triangle of crescent rolls and place one piece of chicken at the wide end of each one. Spread a good layer of the mayonnaise mixture on top of each piece of chicken.
Divide the mozzarella slices in half to create 8 slices, and add to the top of each piece of chicken.
Roll the crescent dough around each piece of chicken and place on the prepared cookie sheet. Melt the remaining tablespoon of butter in the microwave and brush over the tops of each crescent roll. Then sprinkle each roll-up with the remaining grated parmesan cheese.
Bake for 14-15 minutes or until the roll-ups are golden brown.