Preheat the oven to 350°F. Boil the potatoes until soft, then drain them and mash them with the butter, salt, and nutmeg.
Grease a casserole dish with butter, spread the mashed potatoes out in the dish, and smooth out the top. Use the handle of a wooden spoon to draw deep lines in the mashed potatoes, dividing the dish into 6 equal squares. Then use the bottom of a glass to make a circular indentation in each square.
Sprinkle shredded mozzarella cheese in the circular indentations and pour tomato sauce in the dividing lines you made in the mashed potatoes.
For the meatballs, mix the ground beef, onion, parsley, garlic, flour, vegetable oil, egg, salt, and pepper until combined. Divide the ground beef mixture into 6 equal portions. Place 1 portion in the palm of your hand, place a mozzarella pearl in the center, and fold the ground beef mixture around the mozzarella pearl until it's completely enclosed. Repeat with the remaining ground beef portions and mozzarella pearls.
Place 1 stuffed meatball in each indentation in the casserole dish and sprinkle shredded mozzarella over the entire casserole. Transfer the casserole dish to the preheated oven and cook at 350°F for 30 minutes. Garnish with fresh parsley before serving.