Melt the butter in a skillet and swirl to completely cover the bottom of the pan. Layer the turnip slices into the pan, sprinkling each layer with the salt, pepper, and spices. Cook for a few minutes over medium heat until they start to sizzle.
Combine the cream and stock together and pour over the turnip slices. Cover and cook over medium-low heat for 15-20 minutes, until the turnips are mostly cooked through.
Remove the cover and continue to simmer to reduce the liquid. When most of the liquid has reduced (another 5-10 minutes), and the sauce is thickened, sprinkle the Parmesan evenly over the top. Serve hot.