Preheat the oven to 350-degree F. Put 4 oz dried mushrooms in a large bowl. Cover with boiling water. Set aside. Scrub clean the kabocha squash and cut off the top quarter of pumpkins (including stems). Scrape out and discard seeds and fiber. Generously season pumpkin cavities with salt, pepper and freshly grated nutmeg. Put 1 Tb butter in each cavity. In a large sauté pan over medium-high heat, warm 3 Tb olive oil. Add 10 large thinly sliced cipollini onions and cook, stirring, until translucent, 5 minutes. Season with salt. Stir in very thinly sliced unpeeled ¾ lbs of sunchokes and cook 5 minutes, stirring occasionally. Reduce heat to medium, cover and cook 10 minutes. Meanwhile drain mushrooms and roughly chop. Add mushrooms to pan. Cook 2 minutes more. Season mixture to taste with salt, pepper and nutmeg. Stuff squash: Put squash on a rimmed baking sheet or roasting pan. Divide filling between cavities, packing down if necessary. Drizzle olive oil, cover with foil and cook in oven until tender, about 2 hours. Meanwhile in a sauté pan over medium-high heat, melt remaining 1 Tb butter. Add 3 Tb chopped fresh sage and cook 1 minute. Add 1 C fresh breadcrumbs and cook, stirring, until toasted, about 5 minutes. Season with salt and pepper and set aside. When squash is finished baking, remove from oven and mound each with cubed Taleggio cheese. Return to the oven until cheese melts, 5 minutes. Divide breadcrumb mixture over tops and return to oven for 2-3 minutes. Drizzle a little optional white truffle oil over squash. Let rest 5 minutes before serving.