This rich, flavorful soup has a slightly nutty taste and a soft, creamy texture. Note that you may use store-bought, preroasted chestnuts, which come vacuum-packed in jars. However, in our testing, we found that freshly roasted chestnuts tasted best. To roast chestnuts, cut an x through the flat bottom of each nut (this helps with peeling later). Toss chestnuts with salt, pepper, and ⅓ cup canola oil. Spread chestnuts on a baking sheet and roast at 425° until tender, about 25–35 minutes. Return chestnuts to the bowl, toss, and cover bowl tightly with plastic wrap. Cool; then peel.
Chop chestnuts and set aside.
Melt 2 tablespoons butter in a Dutch oven over medium heat. Add onion and carrot and cook until tender, 8–10 minutes.
Add thyme and stir briefly.
Add chicken stock, heavy cream, and 2½ cups chopped chestnuts. Season to taste with salt and pepper. Then simmer 20–25 minutes.
Purée in batches in a blender until smooth. Adjust seasoning to taste if necessary.
While soup is simmering, sauté mushrooms in 2 tablespoons butter over high heat, until slightly crispy but still tender, 8–10 minutes. Set aside.
Pour soup into bowls. Garnish with the remaining chestnuts and mushrooms. Serve hot.