Clean, wash and cut the leek into 8 equal-length sticks. Cook in boiling salted water for about 15 minutes. Clean, clean and slice the mushrooms. Peel and chop onion.
Lift the leek out of the water and let it drain. Heat the oil in a saucepan and sauté the onion and mushrooms. Add stock, milk and processed cheese, bring to the boil while stirring. Season with salt and pepper and pour into an ovenproof dish.
Wrap 1 slice of ham around each leek. Melt butter in a pan, stir in breadcrumbs and season with salt and pepper. Place the leek sticks in the sauce and cover with the crumbs.
Bake in the preheated oven (electric cooker: 250 °C/ convection oven: 225 °C/ gas: level 5) for 10-15 minutes.