Combine the butter and olive oil in a large heavy-bottomed pan over medium heat. Add the onion, celery and carrot. Season with salt and pepper and cook, stirring frequently until the vegetables soften and begin to brown, about 15 minutes.

Add the garlic, then add the beef and pancetta. Cook, stirring occasionally, until the meat is thoroughly browned, about 25 minutes. Stir in the tomato paste and cook for 5 minutes. Add the milk and simmer actively until the milk reduces and is absorbed, about 15 minutes.

Add the wine and simmer until the pan is once again almost dry. Add the tomatoes and stock, adjust the heat so the sauce gently simmers, and cook for 3 hours.

To make the pasta: Blanch the spinach in boiling salted water and shock it in ice water. Drain the spinach, squeeze it as dry as possible, then chop it.

Combine the eggs, flour and blanched spinach in a food processor. Add a pinch of salt and pulse until the dough comes together into a ball. Transfer it to a lightly floured board and knead until it is soft and pliable, about 15 minutes.

Divide the dough in thirds, then stretch and thin each third using a pasta machine, working from the largest to the smallest setting. Once a portion of dough has been stretched, cut it into sheets the size of the baking dish (11 inches or so).

To make the béchamel: Combine the butter, milk and flour in a high-sided, heavy-bottomed saucepan. Bring the contents of the pan to a boil. Watch the pan because the milk has a tendency to boil over.

When the sauce reaches a boil, stir and adjust the heat so it is actively simmering. Cook until the sauce thickens, about 25 minutes. Season the béchamel with salt, pepper and nutmeg and keep warm over low heat; strain immediately before using

Preheat the oven to 350 F.

To assemble the lasagna: Spoon just enough sauce to moisten the bottom into a medium baking dish (a 9x11 will work). Spoon a thin layer of béchamel over the sauce and top with Parmigiano-Reggiano. Cover with two pasta sheets and repeat. Build about 9 layers and end with a generous topping of bolognese, béchamel, then grated cheese. Bake until the lasagna is bubbly, about 25 minutes.

Remove from the oven and set aside to rest for at least 30 minutes before serving.