In a large, deep skillet over medium heat, mix together the cooked turkey meat, cream of chicken soup, cream of broccoli soup, milk, and carrots; season with black pepper. Bring the mixture to a simmer.
Preheat oven to 350 degrees F (175 degrees C).
Place biscuits 1 to 2 inches apart on an ungreased baking sheet. Bake in the preheated oven until biscuits are golden brown, 13 to 17 minutes.
To serve, split the biscuits horizontally, and place onto serving plates; ladle the turkey and sauce over the biscuits.