Preheat oven to 325°F. Peel and chop the potatoes into equal-sized pieces and boil in hot water until soft. Drain the water and mash the potatoes with butter and milk and season with nutmeg. Spread the mashed potatoes over a casserole dish and smooth out the top.
Mix the ground beef, onion, bread crumbs, and parsley and season with salt and pepper.
Cut the eggplant in half and cut off the stem. Lay each eggplant half between two large skewers and slice the eggplant (the skewers will keep the knife from cutting all the way through). Cut the eggplant halves completely after every 6th incision.
Fill the eggplant sections with the ground beef mixture and place them on top of the mashed potatoes in the casserole dish. Pour tomato sauce over the hasselback eggplants, sprinkle shredded mozzarella on top, and cook for 30 minutes until the cheese turns golden brown and starts to bubble.