In a small pot, bring dried mushrooms and stock to boil then reduce heat to a low simmer to reconstitute. Remove mushrooms with a slotted spoon, chop and reserve.
Meanwhile, in Dutch oven or heavy pot, heat EVOO, 4 turns of the pan, over medium-high heat. Add pancetta and cook to lightly browned. Add fresh mushrooms and cook to deeply browned, 12-15 minutes. Add carrot, onions, garlic and herbs, and season with salt and pepper. Cook to soften carrots and onions, 8-10 minutes more, then add tomato paste and stir until fragrant. Add wine and deglaze pot, add chopped porcinis and their stock leaving behind the last few tablespoons of liquid where grit may have settled. Stir in milk and bring sauce to a boil. Reduce heat and simmer to thicken, 45 minutes to an hour.
For the filling, combine spinach in a bowl with the milk to loosen it up. Stir in half the Parm cheese, all of the ricotta and season with salt, pepper and nutmeg. Add in beaten eggs and stir to combine.
For the bechamel, heat a small sauce pot over medium heat with butter. Whisk in flour then milk. Bring to a boil then reduce heat to simmer. Season with salt, pepper and nutmeg and thicken a few minutes until sauce coats spoon.
Preheat oven to 400F.
In a baking dish, add 1/3 of mushroom sauce, top with 3 sheets of pasta and layer in half of the spinach filling. Top the spinach with another 1/3 of the mushroom sauce then cover that with 3 more sheets of pasta. Repeat with remaining half of spinach and last of mushrooms sauce, top with 3 more sheets of pasta. Cover top layer of pasta with white sauce in an even layer and sprinkle with remaining 1/2 cup Parm cheese. Cover with parchment or plastic then foil and bake for 45 minutes. Remove foil and bake to golden, 10-15 minutes more. Let stand up to 30 minutes before cutting.