Heat the butter in a 3-quart saucepan over medium heat. Add the shallots, chestnuts, figs and celery and cook until the celery is tender, stirring occasionally.
Stir the honey and broth in the saucepan and heat to a boil. Remove the saucepan from the heat. Add the parsley and stuffing and mix lightly. Spoon the stuffing mixture into a greased 3-quart casserole. Cover the casserole.
Bake for 30 minutes or until the stuffing mixture is hot.