Finely grate the parmesan. Wash the thyme, shake dry and remove the leaves. Stir starch and cream until smooth. Stir in parmesan and thyme. Season with salt, pepper and nutmeg.
Preheat oven (H-stove: 200°C/circulating air: 175°C/gas: see manufacturer). Quarter pumpkin, remove seeds, peel and cut into thin slices. Wash apples, quarter them, remove seeds, also cut into thin slices.
Place the pumpkin and apples in a fan-shaped form in a greased flat casserole dish. Pour the cheese cream over it. Bake in a hot oven for 35-40 minutes.