Peel, wash and chop the potatoes. Cook in boiling salted water for about 20 minutes. Clean the mushrooms and slice them into thin slices. Wash and clean spinach and drain well.
Wash the meat and dab dry. Spread 1 slice of ham and some spinach on each piece. Roll them up and fix them with wooden skewers. Season with salt and pepper. Heat 2 tablespoons of oil in a frying pan, fry the rolls all around.
Deglaze with white wine and 200 ml water, bring to the boil and stir in the stock. Cover and stew for about 10 minutes. Drain the potatoes, let them steam briefly. Add milk and fat, mash everything to a puree.
Season to taste with salt and nutmeg. Keep covered warm. Whisk vinegar with salt, pepper and sugar. Stir in 3 tablespoons of oil in a thin stream. Mix remaining spinach and mushrooms with the vinaigrette.
Stir the sauce thickener into the braising liquid, let it simmer for about 1 minute. Season to taste with salt and pepper. Wash parsley, dab dry and cut into fine strips. Sprinkle puree with parsley.
Serve the rolls with sauce, purée and salad.