For the bechamel: Gently heat the milk over a low flame but do not boil. While the milk is heating put the butter into a sauce pot and slowly melt over low heat. When the butter is melted whisk in the flour gradually to avoid lumps and gently cook this roux. Using a wire whisk, very slowly begin to pour the hot milk into the roux, a little at a time. Avoid lumps by going very slowly. When all the milk has been added, add the seasoning, turn the heat very low and cook for 20 minutes. When finished allow to cool somewhat before using in the lasagna recipe.
For the Bolognese: Heat the oil and butter together, over low heat, in a heavy bottomed pot. Add the onion, celery and carrot and cook until wilted. Add the meat and, breaking up the meat with a fork or spoon, cook gently and stirring frequently. Season the meat with salt and pepper, add the wine and allow the wine to cook completely down to almost dry before adding the tomatoes and water. Adjust the heat to a slow simmer and, being careful not to cook too rapidly, cook the meat and tomato sauce for between 3 to 4 hours. Stir frequently to avoid scorching the bottom of the pot and keep an eye on this simmering pot. When the sauce has cooked for several hours and the excess water has cooked off, remove from the heat and allow to cool before assembling the lasagna.
For the pasta: Bring the 12 quarts water to the boil. Before cooking the pasta have all the equipment and ice water ready for the cooking and chilling process. Add the salt to the pasta pot, reboil and begin to blanch or parcook the pasta in batches. Cook each batch for 2 to 3 minutes in rapidly boiling water before using a large wire strainer to scoop out the cooked pasta, submerge in the ice water and then resume cooking another batch of pasta using the same method. Small bathes ensure uniform cooking and cooling. When the pasta sheets have cooled in 1 or 2 minutes, remove them from the water and place them on paper towels to dry. When all the pasta has been cooked in this manner the lasagna may be assembled.
To assemble and bake the lasagna:
Preheat the oven to 375 degrees.
Spread some bechamel on the bottom of the baking pan. Top with a layer of pasta sheets. Spread a thin layer of meat sauce on top of the pasta, top with a layer of bechamel, evenly sprinkle on some grated Parmigiano cheese and top with another single layer of pasta. Do this layering process until all of the ingredients have been used and making sure that the final and top layer is bechamel sauce with Parmigiano sprinkled on. When the baking dish is completely filled the lasagna is ready to be baked. Place into the oven and bake for 45 minutes until the top has browned and the edges are crispy.