Preheat oven to 350 degrees F (175 degrees C). Lightly grease a medium casserole dish.
Prepare the stuffing according to package directions.
Place turnip and carrots in a pot with enough water to cover, and bring to a boil. Cook until tender. Drain, and mash. Mix in butter and brown sugar until melted.
Place processed cheese food in a microwave-safe bowl, and melt in the microwave. Stir in milk, and mix into the mashed vegetables. Transfer to the prepared casserole dish. Top with the stuffing.
Bake 20 minutes in the preheated oven, until golden brown.
