1. Preheat the oven to 325F.

2. Melt the butter in a 4-quart saucepan over medium-high heat. Add the mushrooms, onion, savory and nutmeg and sauté until the vegetables are tender, about 3 minutes. Remove from heat. Add the broccoli, stuffing mix, broth and wild rice and mix well.

3. Fill the cavities of the turkey loosely with the stuffing, reserving the remaining stuffing. Place the turkey, breast side up, on a rack in a roasting pan.

4. Spoon the reserved stuffing into an 8 by 8-inch baking pan. Chill, covered, until time to bake.

5. Roast the turkey, basting occasionally with pan drippings, until an instant-read thermometer inserted in an inner thigh and in the stuffing registers 180F, about 4 hours. Place the uncovered reserved stuffing in the oven during the last 40 minutes of turkey baking time, until browned on the top and heated through.