Grate cheese. Cut broccoli into florets from the stalk and wash. Peel, wash and slice the carrots. Cut ham into strips. Peel and wash the potatoes and cut them into 4 mm thick slices with a kitchen slicer or knife.
Layer vegetables, potatoes and ham in a greased casserole dish (approx. 1.5 litres capacity). Wash the marjoram, shake dry, except for something to garnish, pluck leaves from the stalks and chop.
Whisk eggs and milk. Season well with salt, pepper and nutmeg. Pour egg milk over the casserole. Sprinkle with cheese and cook in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for about 40 minutes.
Garnish with marjoram.