Generously peel, quarter and thinly slice the turnip. Peel the onions and cut into wedges. Heat 2 tablespoons of oil in the pan. Stew the turnip slices in it for about 5 minutes. Season to taste with salt, pepper and balsamic vinegar. Arrange on plates and let cool down.
Heat the rest of the oil. Steam the onions and rosemary in it until soft. Season to taste with honey, salt, pepper and white wine vinegar. Serve with the turnips.