Pour off the fat from the skillet and add the remaining 1 tablespoon of butter. Add the mushrooms and shallot and cook over moderate heat, stirring, until softened, about 4 minutes. Add the wine and Cognac and simmer over moderately high heat until almost dry, about 3 minutes. Add the cream and stock and simmer until thickened, about 8 minutes. Stir in the mustard and dill and season with salt and pepper. Add the chicken to the sauce, skin side up, along with any accumulated juices. Simmer over low heat until the chicken is warmed through, about 2 minutes. Spoon the sauce onto plates, top with the chicken and serve.