Cut each large schnitzel into 3 to 4 smaller pieces. Season with salt and pepper. Dip each piece in beaten egg, then coat in breadcrumbs. Fry in a pan over medium-high heat until golden brown on both sides (about 5 minutes). Cool on a plate.
Roughly chop onions and sauté in a pan with a small amount of butter over medium heat until translucent (about 6 minutes). Squeeze and add the garlic clove. Cut ham into strips and add with mushrooms. Stir in sweet cream and season with salt, pepper, and broth or broth powder to taste. Cool to room temperature. Alternatively: sauté 6 onions in butter, add one package of onion soup, omit the garlic/salt/pepper, add soup spices to taste, and cool.
Layer the schnitzel pieces in a casserole dish. Pour the marinade over them. Cover with a lid and refrigerate for 12 hours.
Place the covered casserole in a 225°C (437°F) oven without preheating and bake for 1 hour 30 minutes. Remove the lid, sprinkle Parmesan cheese over the schnitzel, add a few small flakes of butter, and bake uncovered for another 10 minutes.