Serves 6 to 8
Make the Bolognese sauce: Heat butter over medium-high heat in a large pot. Add bacon and ham and saute until caramelized and light brown, about 10 minutes. Add ground meats and cook over high heat until well browned, stirring constantly, about 20 minutes. Add onions, carrots, celery, and mushrooms and cook until soft, about 5 minutes. Add garlic, allspice, cinnamon, and nutmeg to the pan and cook for 2 minutes. Add tomato paste and cook for 2 minutes. Add wine and cook until almost evaporated. Add stock and simmer over medium-high heat until sauce is thickened and flavorful, about 45 minutes to one hour. Season with salt and pepper. Add chicken livers and cook 5 minutes. Stir in cream and parsley, and adjust seasoning if necessary. Set aside until ready to assemble lasagna.
Preheat the oven to 350 degrees.
Make the bechamel: In a saucepan, melt butter over low heat and stir in flour, stirring constantly until smooth, about 2 minutes. Slowly whisk in milk, stirring vigorously to blend together. Set over high heat and quickly bring to a boil for 1 minute, stirring. Allow to cook another 5 minutes, or until floury taste no longer remains. Remove from heat and stir in salt, pepper, and nutmeg.
Butter a 9- by 13-inch baking dish, then spoon 1/2 cup of meat sauce onto the bottom of the dish. Cover with sheets of fresh pasta. Top with a layer of meat sauce (making certain that pasta is completely covered), a layer of bechamel sauce, then a light dusting of cheese. Repeat layering lasagna, sauces and cheese in this manner until all have been used, ending with a topping of bechamel sauce and cheese.
Bake until the lasagna is bubbling and golden brown, about 1 hour. Allow to rest 10 minutes before serving.
Chef's note: I love making this lasagna with sheets of fresh pasta, usually available at upscale Italian groceries. If you cannot find fresh pasta sheets and don't want to go through the trouble of making them at home, feel free to substitute regular (precooked) lasagna noodles.