Tenderize the steaks with a mallet. Mix all the ingredients for the marinade in a bowl and put the steaks in it. Put it in the fridge for a few hours. Lay out an oval oven-safe bowl with foil.
Arrange the pork steaks along the bottom and sides of the bowl so that the edges of the meat spill out of it. Grate the carrots and onions and distribute 1/2 of them over the steaks. Grate the ham and some of the cheese. Stir well and fill the mushrooms with them.
Arrange the stuffed mushrooms on top of the onions and carrots. Arrange the chicken fillets on top. Sprinkle with the rest of the onions, carrots and finish off with grated cheese. Fold the edges of pork steaks inward.
Cover with foil and bake at 347°F (175 °C) for about 2 hours. Take the bowl out of the oven and transfer the large "meatball" into an oven dish. Bake it for 10 min. or so, so that it gains a nice golden crisp.