Prep the oven and pan: Preheat your oven to 375°F (190°C). Line a large baking sheet with parchment paper or spray lightly with non-stick cooking spray.
Mix the filling: In a medium bowl, combine the shredded chicken, softened cream cheese, mayonnaise, finely chopped celery, garlic powder, salt, and black pepper. Stir until the mixture is well combined and holds together.
Prepare the dough: Unroll the crescent dough. If using triangles, press two triangles together to form a rectangle, or use crescent sheet dough cut into 6 equal portions.
Stuff and seal: Place one slice of mozzarella cheese in the center of each dough portion. Top with a generous scoop (about 1/3 cup) of the chicken mixture. Carefully fold the dough corners over the filling, pinching the seams tightly to seal the chicken and cheese inside.
Bake: Place the stuffed rolls seam-side down on the prepared baking sheet. Bake for 12 to 15 minutes, or until the dough is light golden brown.
Add the cheesy crust: Carefully sprinkle the shredded mozzarella cheese over the top of each roll. Return to the oven for an additional 3 minutes, or until the topping cheese is completely melted, bubbling, and beautifully browned.
Serve: Let cool for 5 minutes before serving to let the cheese set slightly. Serve warm to enjoy that incredible cheese pull!