For the Bolognese sauce: Heat the butter and oil in a large Dutch oven or other heavy-bottomed pot over medium heat. When the butter is melted and begins to sizzle, stir in the carrot, celery, onion and parsley. Reduce heat to medium-low and cook, stirring often, for 10 minutes, or until the vegetables are soft and golden. Mix in the beef, pork and veal and use a wooden spoon or spatula to break up the large pieces of meat. Cook over medium-low heat, stirring often, until the meat has turned deep brown and is crumbly but still tender. This will take longer than you think, at least an hour to 90 minutes.
When the meat is ready, increase the heat to medium-high and add the wine, stirring for a minute or two until it is absorbed. Return the heat to medium-low and season with about 1 teaspoon salt, pepper to taste, and the nutmeg. Stir in the milk and cook until it has been mostly absorbed, about 3 minutes. In a small bowl, dilute the tomato paste in a little of the beef broth and add it to the pot. Add the remaining broth and mix well. Cover partially, reduce the heat to low, and let simmer slowly for 2 hours or more, until it is very thick and all of the vegetables have more or less melted into the sauce. Stir in the cream and mortadella and cook at a gentle simmer until heated through.
The sauce is ready to use or you can cool and transfer to a container; refrigerate for up to 3 days or freeze for up to 6 months.
For the lasagna: Spread a clean tablecloth on a table or clean flat surface near the stove. Have ready the uncooked pasta, béchamel, Bolognese sauce, and Parmigiano cheese.
Preheat the oven to 375 degrees. Lightly coat a 9- by 13-inch lasagna or baking dish (or 2 smaller baking dishes) with the butter.