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In a large saucepan, melt 6 tablespoons of the butter over medium heat. Add the shallot, carrot, and celery, and cook until softened, about 5 minutes. Sift the flour over the vegetables, and cook the mixture, stirring constantly with a wooden spoon until it lightens in color, 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 plastic wrap on the surface of the sauce and set aside until ready to assemble the lasagna. (The sauce can be made a day ahead and refrigerated. Reheat before assembling the lasagna. )

Meanwhile, cook the noodles. Bring a large pot of water to a boil, season generously with salt, and boil the lasagna noodles according to package instructions. Drain. Spread the noodles out and layer between pieces of plastic wrap. Set aside.

Preheat the oven to 350 degrees F. Butter an ovenproof 9 x 13-inch casserole dish.

Cover the bottom of the pan with a layer of noodles. Cover with 1 1/2 cups of the meat sauce, 1 cup of the white sauce and 3 tablespoons of the cheese. Repeat to make 3 more layers ending with the remaining meat sauce, white sauce, and cheese. Dot the top with the remaining tablespoon 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.