1 to 1 1/2 pound chicken bones (from 2 cooked chickens), broken into 2- to 3-inch pieces
4 cups low-sodium chicken broth
1 carrot, thinly sliced
1 medium onion, coarsely chopped
2 celery ribs, cut into 1-inch pieces
2 garlic cloves, smashed
5 whole black peppercorns
1 Turkish or 1/2 California bay leaf
2 whole cloves
3/4 stick (6 tablespoons) unsalted butter
3/4 pound mushrooms, thinly sliced
1/2 teaspoon salt
1/4 teaspoon black pepper
2 tablespoons all-purpose flour
1 cup heavy cream
3 tablespoons medium-dry Sherry
2 tablespoons truffle butter* (optional)
1/2 lb spaghetti
2 pounds chicken meat (from 2 cooked chickens), torn into 1-inch pieces
1 ounce freshly grated Parmigiano-Reggiano (1/2 cup)