Preheat oven to 375 degrees F (190 degrees C). Spray into an 8x8-inch casserole dish with cooking spray.
Place turnips into a large pot and cover with chicken stock; bring to a boil. Reduce heat to medium-low and simmer until tender, about 25 minutes; drain. Transfer turnips to a bowl and mash with a potato masher or fork.
Melt 3 tablespoons butter in a frying pan over medium-low heat; cook and stir bread crumbs in the melted butter until butter is absorbed, 2 to 3 minutes. Remove from heat.
Stir 2 tablespoons butter, egg yolks, brown sugar, baking powder, salt, black pepper, and mace into mashed turnips. Beat egg whites in a metal or glass bowl using an electric mixer until fluffy; fold into turnip mixture. Pour turnip mixture into the prepared casserole dish; sprinkle with bread crumb mixture.
Bake in the preheated oven until souffle is puffed up and set in the middle, about 25 minutes. Serve immediately.