Preheat the oven to 400°F.
Using a sharp paring knife, make a long slash on the flat side of each chestnut, cutting through the outer shell and inner brown skin.
Place chestnuts on a rimmed baking sheet and roast until tender when pierced with a fork, about 1 hour.
Every 15 minutes, sprinkle the chestnuts with a little water.
While the chestnuts are roasting, place the onions and carrots in a 9-by- 13-inch baking pan.
Drizzle with the olive oil and toss the vegetables so they are thoroughly coated.
Roast until tender when pierced with a fork, about 1 hour.
Let cool while you peel the chestnuts.
Peel the chestnuts while they are still quite warm, but cool enough to handle.
Using a sharp paring knife, remove the outer shell as well as the inner brown skin.
Discard any chestnuts that look rotten.
Set aside the chestnuts that are hard to peel and rewarm in a 400°F oven; or place on a paper towel and rewarm in a microwave for 45 seconds on high.
Repeat if necessary.
Combine the chestnuts and roasted vegetables in a medium mixing bowl.
Place one-fourth of the mixture in a blender or in a food processor fitted with the metal blade.
Add 2 cups of the stock.
Process until the puree is uniformly coarse rather than smooth in texture.
Pour into a 4-quart saucepan.
Repeat 3 more times with the remaining chestnut and vegetable mixture and the stock.
Add the salt and a few grinds of pepper to taste.
Heat to a simmer and cook about 20 minutes to meld the flavors.
Add the cream, stir to combine, and remove from the heat.
Taste and add more salt or pepper if desired.
Keep the soup warm while you make the mushroom garnish, or cool and refrigerate, covered, up to 3 days prior to serving.
TO MAKE THE MUSHROOM GARNISH Melt the butter in a 10-inch saute pan over medium-high heat.
Add the mushrooms, raise the heat to high, and saute, stirring constantly, for 2 minutes.
Add the thyme and parsley and saute until the liquids evaporate and the mushrooms are lightly browned, 2 minutes longer.