Peel, wash and grate the potatoes. Stir egg yolk and 1 tbsp. flour into the potatoes and season with salt and nutmeg. Heat 2 tablespoons of oil in portions in a frying pan. Fry about 8 portions of the potato mixture at medium heat until golden brown.
Remove the finished Rösti and let them drip off on kitchen paper. Peel and finely dice the shallot. Clean and clean the mushrooms and cut them into thin slices. Heat 2 tbsp. oil, fry the mushrooms for 2-3 minutes, turning them, and season with salt and pepper.
Add the shallot to the pan after about 1 minute. Dust with 1/2 tbsp. flour and sauté briefly. Add cream, stock and white wine and simmer for 3-4 minutes. Wash parsley, dab dry, remove leaves and cut finely, except for a little bit for garnishing.
Stir the parsley into the mushroom sauce and set aside. Wash the meat, dab dry and season with salt and pepper. Heat 2 tablespoons of oil in a frying pan. Fry the meat in portions for about 3 minutes, turning.
Place the Rösti on a baking tray lined with baking paper. Cover each with 1 medallion, mushroom sauce and 1 slice of cheese. Bake in a preheated oven (electric range: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 5 minutes.
Remove, arrange and garnish with the rest of the parsley. Serve immediately.