Preheat oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole.
Bring a pot of water to a boil and add turnips. Reduce heat to low, and simmer turnips until tender, about 15 minutes.
Drain.
Transfer turnips to a large bowl and mash with applesauce, 6 tablespoons softened butter, brown sugar, eggs, salt, black pepper, and half the bread crumbs. Spoon turnip mixture into the prepared casserole dish, and sprinkle with remaining half of bread crumbs.
Drizzle with 2 tablespoons melted butter.
Bake in the preheated oven until set, about 30 minutes.
