Preparing the Chestnuts
If using fresh chestnuts, make a small incision in the skin of each chestnut to prevent them from exploding while cooking.
Boil the chestnuts in water for about 10 minutes. Once cooled, peel the shells and the inner skin. If using canned chestnuts, drain and rinse them under cold water.
Sautéing the Vegetables
In a large pot, heat the olive oil over medium heat.
Add the chopped onion, garlic, carrot, and celery. Sauté until the vegetables are soft and fragrant, about 5-7 minutes.
Cooking the Chestnuts
Add the peeled chestnuts to the pot and stir to combine. Cook for an additional 5 minutes.
Pour in the broth, ensuring that the chestnuts are fully submerged.
Season with salt and pepper to taste.
Simmering
Bring the mixture to a boil, then reduce the heat to low. Let it simmer uncovered for about 20-25 minutes, allowing the flavors to meld together.
Blending the Dish (Optional)
For a creamier texture, use an immersion blender to puree some of the chestnuts and vegetables directly in the pot. Alternatively, transfer half the mixture to a blender, blend until smooth, and return it to the pot.
Serving
Allow the dish to stand for about 10 minutes before serving.
Serve warm, garnished with fresh herbs and grated Parmesan cheese if desired.