Heat butter in a large saucepan, stir in flour and sauté briefly. Add stock and cream and let simmer for about 5 minutes while stirring. Grate cheese and stir 50 g into the sauce.
Season to taste with wine, salt and pepper.
Toast the bread in the toaster until golden brown. Put 4 slices of toast on a baking tray and cover with some sauce. Place the slices of ham folded on top and also cover with the sauce. Place the remaining slices of toast on top and pour the remaining sauce over them.
Sprinkle with the remaining cheese. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for approx. 3 minutes.
Wash the chives, shake dry and cut into fine rolls. Heat 1 tbsp. clarified butter in a pan. Beat the eggs and let them fry for 2-3 minutes as fried eggs. Season with salt and pepper.
Spread fried eggs on the toast and sprinkle with chives.