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.
I have skipped the bread crumb step before and it just needs to bake for few minutes longer to help firm souffle up.
Yellow turnips are best but white ones work really well too, plus cook faster.