Closely identified with French cuisine, chestnut soups are low in fat. For a velvety smooth texture, pass soup through a fine strainer after the mixture has been processed and before adding the cream.
Preheat oven to 350 degrees. Using a paring knife, make an incision in each chestnut about 1/8-inch deep through the shell and into the flesh, cutting almost all the way around nut. Transfer to a rimmed baking sheet. Roast until chestnuts are tender when pierced with the paring knife, about 35 minutes. Turn off oven. Leaving sheet in oven, remove several chestnuts at a time. Working quickly, place each chestnut in a kitchen towel, and remove and discard shell and inner skin.
Roughly chop all but 2 cremini and 2 shiitake mushrooms. Heat 1 tablespoon butter with olive oil in a small stockpot over medium-high heat. Add chopped mushrooms, and season with salt and pepper. Cook mushrooms, stirring occasionally, until they start to brown, about 5 minutes. Add onion, garlic, and thyme sprigs. Reduce heat to medium-low; cook, stirring occasionally, until onions are translucent, about 8 minutes. Add all but 4 peeled chestnuts, and cook until golden, about 5 minutes. Add stock and the water, raise heat to high, and bring to a boil. Reduce heat; simmer until chestnuts are falling-apart tender, about 1 hour. Remove and discard thyme sprigs, and let soup cool slightly.
Pass soup through a fine sieve into a bowl; transfer solids in batches to a food processor or blender, and puree until completely smooth. Add strained liquid, and process 1 minute. Return soup to stockpot, and season with salt and pepper.
Cut the remaining 4 chestnuts and 4 mushrooms into 1/4-inch-thick slices. Melt remaining tablespoon butter in a small skillet over medium-high heat. Saute sliced chestnuts and mushrooms until crisp and golden brown, 3 to 4 minutes.
Just before serving, heat soup over low. Stir in cream, and remove from heat. Ladle soup into shallow bowls; garnish with sauteed chestnuts and mushrooms and the thyme leaves.
Let cool completely before storing the soup (prepared through step 3) in an airtight container. Thaw frozen soup overnight in the refrigerator. When ready to serve, proceed with steps 4 and 5.