Preheat the oven to 325ºF. Put the pumpkin quarters in a bowl. Add 3 Tbsp of the softened butter, season with salt and pepper, and toss to coat the pumpkin. Spread the quarters out on a rimmed cookie sheet or baking sheet. Roast until tender to a fork-tip, about 50 minutes to 1 hour.
Remove from the oven and, when cool enough to handle, scoop out the flesh. You should have approximately 3 cups of roasted pumpkin.
Put 3 Tbsp butter into a large, heavy-bottomed pot and warm it over low heat. Add the onion, celery, and a pinch of salt. Cook, stirring occasionally, until the vegetables are softened but not browned, approximately 20 minutes. Pour in the stock and add the roasted pumpkin. Bring to a boil over high heat. Lower the heat and simmer for 20 minutes. Whisk in the mascarpone and pumpkin puree.
Warm 2 Tbsp of butter over medium-low heat in a medium, heavy-bottomed sauté pan. Add the shallots and sauté for 3 minutes. Season with salt and 3 grinds of white pepper (or to taste). Set aside, covered, to keep warm.
Working in batches, ladle the soup in a blender and puree until velvety smooth. Season to taste with salt. Continue to blend until smooth. Strain the soup through a fine-mesh strainer set over a bowl. Add the nutmeg, orange zest, and 3 grinds of white pepper to the soup.
Melt the butter over low heat in a heavy-bottomed sauté pan. Stir in the cranberries, sugar, orange zest, Grand Marnier (if using), cinnamon, and ginger.
Cook, stirring occasionally, until the cranberries begin to burst, approximately 6 minutes. The mixture will be bubbling and foamy. Continue to cook for another 3 minutes.
Remove the pan from the heat and let cool. The compote can be covered and refrigerated for up to 1 week.
Divide the soup among 6 wide, shallow bowls. Garnish each serving with 1 heaping tablespoon of cranberry-walnut compote, if desired. Divide the mushrooms equally among the bowls, scattering them over the surface of the soup, and serve.