How to Make It
In a large saucepan, melt 1 tablespoon of the butter. Add the pancetta and cook over moderate heat until lightly browned, about 5 minutes. Add the shallots and celery root and cook until the celery root is just tender, about 10 minutes. Transfer the vegetables to a bowl, leaving the pancetta and fat in the saucepan.
Add the remaining 1 tablespoon of butter to the saucepan along with the mushrooms and all but 2 tablespoons of the chestnuts. Cook over moderately high heat, stirring occasionally, until the mushrooms have released their liquid and are slightly softened, 6 minutes. Add 2 tablespoons of the chicken stock and the celery root mixture and cook for 1 minute. Add the Cognac and cook until evaporated, 2 minutes.
Add the bay leaf, sage and thyme sprigs to the saucepan along with the remaining 3 3/4 cups plus 2 tablespoons of chicken stock. Bring to a boil and simmer for 30 minutes, stirring occasionally. Discard the pancetta, bay leaf, sage and thyme.
Working in batches, puree the soup in a blender until creamy and smooth. Return the soup to the saucepan. Stir in the half-and-half, season with salt and white pepper and keep warm.
In a large bowl, using a handheld electric mixer, whip the cream until soft peaks form. Beat in the grappa and season with salt and pepper.
Ladle the soup into small bowls. Dollop the grappa cream on top, garnish with the thyme leaves and the reserved 2 tablespoons of chestnuts and serve.