Preheat oven to 425°F.
Carve top off the pumpkin, scrape out seeds and clean out cavity. Drizzle with olive oil, salt and pepper. Turn pumpkin upside down and roast 1 hour and 15 minutes. Cool to handle. Slice away skin in strips working from top to bottom, as you would remove skin from a melon. Turn pumpkin right-side up.
Lower oven temperature to 375°F.
Heat a saucepot or Dutch oven over medium-high heat with EVOO, 2 turns of the pan. Add beef and season with salt, pepper, allspice or cloves and sage; brown and crumble. Cut sausage from casings, add to beef, and brown and crumble. Add tomato paste, cook 2-3 minutes. Add the onion, celery, carrot and garlic, and stir to soften, 7-8 minutes. Deglaze the pan with the sweet vermouth, let it cook off then add wine and stock. Simmer 30 minutes until liquid is almost fully evaporated.
Bring a large pot of water to a boil for the pasta.
Melt 4 tablespoons butter in a saucepan then whisk in flour and cook a minute or two. Whisk in milk and season with salt, pepper and nutmeg. Whisk up the eggs in a bowl and add a ladle of the warm sauce to the eggs to temper them. Add all of the eggs to the sauce and let thicken a bit. Stir in grated Parm then remove from heat.
Salt the pasta water and undercook the pasta by 4 minutes from package directions, about 4-5 minutes. Cold-shock and drain well.
In a large bowl, combine the pasta with meat and béchamel sauces, and add in diced cheese. Place the pumpkin in an oven-safe large dish or baking sheet that you can serve from. Fill the pumpkin with the pasta and spray or brush outside with olive oil. Roast for 1 hour. If the pumpkin gets too brown or dry looking, loosely cover with foil.
Melt the remaining butter in saucepan and when it bubbles, add the sage leaves. Crisp leaves and remove to paper towel with a fork. When butter is brown and nutty, remove pan from heat.
Carefully brush or pour the browned butter down over the pumpkin. To serve, cut into wedges and top each slice with a few crispy sage leaves.