Grate cheese. Whisk cream and eggs. Season the glaze with salt, pepper and nutmeg. Cut the croissants horizontally.
Place the lower croissant halves side by side in a greased large casserole dish or deep baking tray. Sprinkle with 1⁄3 cheese and place 2 slices of ham on each. Sprinkle with 1⁄3 cheese and place the lids on top. Pour egg icing over it and sprinkle the rest of the cheese on top. Bake in the preheated oven (electric cooker: 200 °C/circulating air: 180 °C/gas: see manufacturer) for approx. 20 minutes.