Fill a saucepan with 1cm of water, then add pumpkin pieces. Bring to a boil over high heat then reduce heat to medium-low, cover and steam until the pumpkin is very tender, 10 to 15 minutes. Drain pumpkin then mash with 1 tablespoon of butter, cinnamon, salt and pepper to taste then set aside.
Melt 2 tablespoons of butter in a saucepan over medium heat. Whisk in flour and cook, stirring constantly, until the paste just begins to turn golden, about 2 minutes. Whisk in milk gradually so that no lumps form. Bring to a gentle boil. Add the bay leaves then reduce heat to low. Allow to gently cook for 10 to 15 minutes, stirring frequently then remove from heat.
Heat 1 tablespoon olive oil in a large frypan over medium heat. Stir in onion, fennel and garlic; cook until the onion has softened and turned translucent, about 5 minutes. Add spinach and cook until wilted. Scrape mixture into a large bowl and mix well with ricotta cheese and nutmeg.
Using the same frypan, heat another 1 tablespoon olive oil over high heat. Brown mince in oil, mixing thoroughly to break into small pieces. Once browned, reduce heat to medium-low and pour off excess fat. Stir in tomato paste and tomato puree. Gently simmer until thickened, about 10 minutes.
Preheat oven to 200 degrees C. Grease a 23x33 cm lasagne dish.
Line the bottom of the lasagne dish with 4 lasagne sheets, do not overlap. Spread the ricotta mixture evenly over sheets, then sprinkle with 1/3 of the Parmesan cheese. Place another 4 sheets on top of the ricotta, then spread evenly with the mashed pumpkin. Place the remaining 4 sheets on top of the pumpkin and top with the tomato sauce; sprinkle with another 1/3 of the Parmesan cheese. Stir the white sauce until smooth, then discard the bay leaves; pour the sauce over top of the lasagne. Sprinkle with remaining Parmesan cheese.
Place lasagne dish onto a foil-lined baking tray (to catch any spills). Bake in preheated oven until the lasagne sheets have softened and the white sauce has turned bubbly and golden brown, about 30 minutes.
You could also make this a full vegetarian version by omitting the mince and substituting TVP or finely diced mixed vegetables (zucchini, carrot, celery, onion).