Pour 2 cups of boiling water over the dried porcini and let sit while you prep your other steps, 10 to 15 minutes.
Peel, de-seed and medium dice the kabocha squash. Pour onto a baking sheet, sprinkle with salt and pepper and drizzle with 2 tablespoons of olive oil. Roast in the oven for about 30 minutes to cook through.
In the meantime, use a small serrated paring knife to remove the top of the pumpkin wide enough to later fill the pumpkin stuffing and scoop out the seeds.
Dice the baguette and place in the oven on a sheet pan to make croutons, about 5 minutes.
In a large skillet over medium heat cook the Italian sausage breaking it up into little pieces and cook it all the way through. Remove it from the pan leaving the grease. Now add the onions and garlic and cook, stirring, until softened, 5 to 8 minutes.
While the onions are cooking, take the porcinis that are re-hydrating in the hot water, wring them out and give them a rough chop. Remove the cooked onions and put in a large bowl with the Italian sausage. In the same skillet, add the sliced white mushrooms, chopped porcinis along with 1/2 cup of the mushroom liquid and cook for about 5 minutes. Remove and add to the large bowl with the sausage mixture.
Add the cooked kabocha and croutons to the sausage bowl. Mix well and add the ginger, paprika, nutmeg, salt and pepper.
Add the milk and heavy cream to a saucepan and bring it to a simmer.
To assemble: Sprinkle the inside of the pumpkin with salt and pepper. Add a layer of the sausage mixture, some of the heated milk-cream mixture, add a layer of Gruyere and continue by pressing down repeating the layering process until the pumpkin is completely full. Place the top of the pumpkin back on, put it in a 9- by 13-inch baking dish and fill with 1- to 2-inches of warmed water. Bake until it's cooked through, about 1 1/2 hours
Serve by scraping the inside of the pumpkin and getting some of the pumpkin flesh along with the filling to serve warm.