Make Bolognese Sauce

1. Heat oil in a 12- to 14-inch heavy skillet over medium heat until it shimmers. Cook pancetta, onion, carrot, celery, and garlic, stirring occasionally, until vegetables are golden and softened, 12 to 15 minutes.
2. Add beef and cook, stirring occasionally and breaking up any lumps, until meat is no longer pink, 6 to 10 minutes.
3. Stir in wine, milk, tomato paste, thyme, 1/4 tsp salt, and 3/4 tsp pepper.
4. Simmer, uncovered, stirring occasionally, until most of liquid has evaporated but sauce is still moist, about 1 hour.

Make Ricotta Filling

1. Put spinach in a sieve and squeeze out as much moisture as possible.
2. Whisk together ricotta, eggs, parmesan, nutmeg, 1 1/4 tsp salt, and 1 tsp pepper. Transfer 1 1/2 cups ricotta mixture to another bowl and whisk in 1/4 cup milk; set aside.
3. Whisk spinach into remaining filling with remaining 1/2 cup milk.

Assemble-Bake Lasagne

1. Preheat oven to 375°F with rack in middle.
2. Spread 1 1/2 cups bolognese sauce in a baking pan and sprinkle with 1 Tbsp parmesan. Cover with 3 noodles, leaving space in between. Spread half of spinach filling on top, then 1 cup bolognese sauce, and top with 1 Tbsp parmesan and 3 noodles; repeat. Top with remaining bolognese sauce, 1 Tbsp parmesan, and remaining 3 noodles. Pour reserved ricotta mixture over top and sprinkle with remaining 1/4 cup parmesan.
3. Cover pan tightly with parchment paper and foil (or just buttered foil) and bake for 50 minutes. Remove foil and bake until the top is browned in spots, about 15 minutes more. Let stand 15 to 30 minutes before cutting.