Heat the olive oil and butter over medium heat in a large heavy-bottomed pot. 

Add the carrot, onions, celery, and garlic and cook, while stirring, until translucent, about 10 minutes.

Add the veal, pork, and pancetta, and turn the heat to high. Use a wooden spoon to stir and break up the meat until it’s very browned, about 20 minutes. 

Add the tomato paste and stir until it deepens slightly in color, about 3 minutes. 

Add the wine, scrape up any browned bits from the bottom of the pan and cook until it's reduced by more than half.

Add the milk and stir until it comes to a boil. Reduce the heat to low, cover, and simmer for 1 ½ to 2 hours. Season with salt and pepper and set aside. 

Place the spinach in a dish towel and squeeze it to remove as much liquid as possible. Puree the spinach in a food processor or finely chop by hand.

Pour 3 ½ cups of flour into the center of a large workspace, making a well in the center. 

Add the eggs, spinach, and ½ teaspoon of olive oil to the well and gently start beating the eggs with a fork.

Slowly begin incorporating the flour from the inner rim of the well, being careful to retain the sides of the well so that the egg mixture does not escape.

Once most of the flour is moistened, start kneading the dough until it's elastic and slightly sticky (for about 5 to 6 minutes), adding a bit more olive oil if it's too dry. Wrap the dough in plastic and allow it to rest for 30 minutes at room temperature.

Bring a large pot of water to a rolling boil, and season liberally with salt. Set up an ice bath next to the stove. 

Working in batches, cook the strips of pasta for one minute, then immediately shock them in the ice bath. Drain well on towels and set aside.

Make a roux by melting butter in a medium saucepan, then whisk in the flour until smooth. Cook while stirring over medium heat for about 5 minutes, until the mixture is light golden brown. 

Add milk to the roux 1 cup at a time, whisking continuously until very smooth, then bring the mixture to a boil. Cook for about 2 to 3 minutes, then remove from the heat. 

Season the sauce with nutmeg, salt and pepper to taste.

Preheat the oven to 375 degrees F. 

Ladle a small amount of ragu in a 9x13 inch baking dish and spread it out to cover, then top with a sprinkling of grated parmesan cheese. 

Assemble the lasagna by layering sheets of pasta, then a thin layer of béchamel sauce, then a thin layer of ragu and a sprinkle of parmesan cheese. Repeat until all sauce and pasta are used up, finishing with a top layer of pasta with béchamel over it. Top with lots of grated parmesan. 

Bake for about 30 to 45 minutes, or until bubbling and browned around the edges. 

Remove from the oven and allow to cool for at least 15 minutes before slicing.