1. 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.

2. 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.

3. 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.

4. 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.

5. 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.