Sauté onion, carrot, and celery in olive oil over medium heat until softened.
Add ground beef and pork, browning thoroughly while breaking up clumps.
Deglaze the pan with dry red wine and simmer until the liquid has mostly evaporated.
Stir in tomato paste and crushed tomatoes, then reduce heat to low and simmer for 2 hours, adding milk in increments to tenderize the meat.
Prepare a béchamel by melting butter in a saucepan, whisking in flour to create a roux, and gradually adding 1 liter of milk while stirring until thickened.
Season the béchamel with salt, pepper, and ground nutmeg.
Preheat oven to 180°C (350°F).
Spread a thin layer of meat ragù in a 9x13 inch baking dish.
Layer lasagna sheets, ragù, béchamel, and Parmigiano-Reggiano; repeat for at least 4 layers.
Top the final layer with béchamel and the remaining cheese.
Bake for 45 minutes until the surface is golden brown and bubbling.
Allow the lasagna to rest for 15 minutes before slicing.