Place mashed potatoes in a bowl; add egg, butter, grated Parmigiana cheese, a pinch of salt, pepper & nutmeg. Combine well. Divide mixture into 8 equal patties. Roll into balls & then flatten into patties. In the center of 4 of the patties place 1/4 of the mushroom mixture. Top mushrooms with a cube of mozzarella cheese. Place one of the remaining potato patties on top of each filled one & gently press edges to seal.