Begin by heating the vegetable oil and 3 tablespoons of butter in a large heavy-bottomed pot or Dutch oven over medium heat.
Add the minced onion, carrot, and celery (the soffritto).
Sauté these vegetables for about 8 to 10 minutes until they are soft and translucent, but not browned.
Increase the heat to medium-high and add the ground beef and ground pork.
Use a wooden spoon to break the meat into very small crumbles.
Cook until the meat is no longer pink and has started to brown slightly.
Stir in the tomato paste and garlic, cooking for another 2 minutes
Pour in the white wine (if using) or a splash of broth to deglaze the pan, scraping up any browned bits from the bottom.
Once the liquid has mostly evaporated, pour in the 1 cup of whole milk.
Simmer the milk with the meat until it has evaporated.
Finally, add the crushed tomatoes and the beef broth.
Reduce the heat to the lowest setting and simmer, partially covered, for at least 2 to 3 hours.
In a medium saucepan, melt 4 tablespoons of butter over medium-low heat.
Once the butter is foaming, whisk in the all-purpose flour.
Cook this mixture (the roux) for about 2 minutes, stirring constantly to remove the "raw" flour taste without letting it brown.
Slowly pour in the whole milk, one cup at a time, whisking vigorously after each addition to prevent lumps.
Continue to cook and stir over medium heat until the sauce thickens enough to coat the back of a spoon.
Remove from heat and stir in the salt and nutmeg.
Cover the surface directly with plastic wrap to prevent a skin from forming.
If using traditional dry lasagna noodles, bring a large pot of salted water to a boil.
Cook the noodles for 2 minutes less than the package directions
Drain and lay them out in a single layer on clean kitchen towels or parchment paper to prevent sticking.
Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with butter.
Base Layer: Spread a thin layer of ragù on the bottom of the dish.
Pasta: Place a layer of noodles over the sauce, slightly overlapping them.
Sauce Duo: Spread a layer of ragù over the pasta, followed by a thin, even layer of béchamel.
Cheese: Sprinkle a generous tablespoon of Parmesan cheese over the béchamel.
Repeat: Repeat these layers until all ingredients are used, usually resulting in 5 to 6 layers.
The Crown: The final layer should be a generous coating of béchamel topped with the remaining Parmesan cheese.
Cover the baking dish tightly with aluminum foil, ensuring the foil does not touch the cheese (you can use toothpicks to prop it up).
Bake for 25 minutes.
Remove the foil and bake for an additional 15 to 20 minutes, or until the top is bubbling and deep golden brown.
