1) In a large saucepan, melt 90g of the butter over medium heat. Add the shallot, carrot and celery, and cook until softened, about 5 minutes.
2) Sift the flour over the vegetables and cook the mixture, stirring constantly with a wooden spoon until it lightens in colour, about 2 minutes. Slowly whisk in the milk and bring to a boil. Add the parsley, thyme and bay leaf. Reduce the heat to low, and simmer, whisking occasionally, until the sauce is thickened, about 30 minutes. Strain and season with 1/2 teaspoon of the salt, nutmeg and pepper to taste. Place cling film on the surface of the sauce and set aside until ready to assemble the lasagne. (The sauce can be made a day ahead and refrigerated. Reheat before assembling the lasagne.)
Meat and tomato sauce:
1) In a large soup pot or Dutch oven, heat the olive oil over medium heat. Add the red pepper flakes and cook for 15 seconds. Add the onion and cook, stirring occasionally, until golden brown, about 15 minutes. Add the garlic and cook until fragrant, about 1 minute.
2) Stir in the tomato puree and cook, stirring constantly, for 1 minute. Add the tomatoes one at a time, crushing them by hand as you go. Season with 1 teaspoon of salt and pepper to taste. Simmer the sauce over low heat, covered.
3) Meanwhile, heat a large skillet over medium-high heat. Add the beef, pork, veal, savory, thyme, oregano and fennel seeds. Season with 1 teaspoon of salt and pepper. Break up the meat with a wooden spoon and cook until it loses its raw colour, about 7 minutes. Add the meat to the sauce, holding back any excess fat. Add the rind of the Parmesan, if using. Simmer the sauce, covered, over low heat for 1 1/2 hours. (If the sauce gets too thick, adjust the consistency with water.) Season with salt and pepper to taste. Just before serving, remove the Parmesan rind and add the grated cheese.
1) While the sauces are cooking, cook the noodles. Bring a large pot of water to the boil, season generously with salt, and boil the lasagne noodles according to package instructions. Drain. Spread the noodles out and layer between pieces of cling film. Set aside.
2) Preheat the oven to 180C/Gas 4. Butter an ovenproof 23 by 33-cm casserole dish.
3) Cover the bottom of the pan with a layer of noodles. Cover with 350ml of the meat sauce, 250ml of the white sauce and about 25g of the cheese. Repeat for three more layers, ending with the remaining meat sauce, white sauce and cheese.
4) Dot the top of the lasagne with the remaining 15g of butter. Bake until bubbly and hot, about 45 to 50 minutes.
Remove from the oven and set aside for 10 minutes to firm up before serving.