Sauté the onion in the lard until lightly browned in an ovenproof pot. The original recipe contains neither tomatoes nor garlic, but they've crept in over the years. Therefore add them, together with the tripe, a few drops of oil, salt, pepper, parsley, and the spices (cloves to taste). Stir well to combine and remove from the fire when all is heated through.
Pour the contents of the pot into a bowl. Don't wash the pot, but rather refill it, layering it with the eggplant, the tripe, and then the ground meat; dust the meat with some grated caciocavallo (don't put all of it into the filling, however), then repeat with more layers until all is used up. Sprinkle the oil over the top and spread the hard boiled eggs over it too.
Lightly beat the fresh egg and mix the remaining caciocavallo into it, together with salt, pepper, and a little more parsley. Spread this mixture over the top and bake in the oven (400 F, 200 C) until it is nicely browned.