Put enough freshly roasted shoulder of lamb through food chopper to make 2 1/2 cups. Cut 3 medium eggplants into 1/4 inch slices and soak in salted water for 1 hour. Drain and dry slices. Saute in enough olive oil to cover bottom of skillet, adding more oil as needed.
Slice thinly 2 medium onions and 5 or 6 mushrooms. Saute them slowly in 2 tablespoons butter until golden brown. Saute 6 fresh tomatoes, peeled, seeded and chopped, in butter.
Put a layer of eggplant in bottom of a baking dish. Add layer of meat, then layer of onions and mushrooms. Pour 1/2 cup of the sauce and tomatoes over the onions. Continue layering, finishing with eggplant and mushrooms and topping with 1 cup tomatoes or enough to fill dish 3/4 full.
Bake at 350 degrees for 45 minutes (until eggplant is tender). Sprinkle with chopped parsley. Stir the yolks of 2 eggs into 1/2 cup heavy cream and pour it in the center. Return dish to oven and bake until the custard is set and the top lightly browned.