Preheat oven to 400ºF. Roll out the crescent sheets and separate into diamond shaped sections. Place a small handful of chicken on each diamond, fold dough over and press ends together to create dumplings. Cut up any excess dough into strips.
Line a 9×13 baking dish with one layer of dumplings. Mix together the soups and broth and layer over dumplings. Cut remaining dough into strips and lacy in a crisscross pattern on the top of the dumplings and soup mixture, season dish with salt and ground black pepper and bake until the dumplings are tender and cooked through and the top is bubbly and brown, about 30 minutes