Add tomato paste, parsley, and lamb Stock. Simmer until liquid is absorbed. Remove from heat. Stir in cinnamon, eggs, cheese, and 1/2 of the bread crumbs.
Melt 6 Tbsp. butter in a saucepan over low heat. Stir in flour. Slowly stir in milk. Continue to cook until the sauce is thick. Add nutmeg. Stir small amount of sauce into the egg yolks. Stir egg yolks into sauce. Cook for 2 minutes, stirring constantly. Remove from heat. Brown eggplant in olive oil over medium-high heat.
Grease a large casserole dish. Sprinkle rest of bread crumbs in bottom of dish. Add layer of eggplant slices. Add some ground lamb. Continue to layer.
Cover with sauce and grated cheese. Bake at 350 degrees for 1 hour.