Preheat the oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish.
Place chicken cubes evenly into the prepared dish.
Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, 5 to 10 minutes. Drain and mash. Add sour cream, Cheddar cheese, butter, carrot, Parmesan cheese, onion soup mix, garlic salt, and pepper; mash together until smooth. Spoon over chicken and sprinkle with bread crumbs.
Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, about 60 to 75 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).