Preheat oven to 325°. Remove giblets and neck from turkey, and rinse turkey with cold water. Drain cavity well; pat dry. Loosen and lift skin from turkey breast without totally detaching skin. Rub 1/4 cup Béarnaise Butter under skin; replace skin. Sprinkle cavity and outside of turkey with desired amount of salt and freshly ground pepper.
Place turkey, breast side up, on a lightly greased roasting rack in a large roasting pan. Tie ends of legs together with string; tuck wingtips under. Rub entire turkey with 1/4 cup Béarnaise Butter. Pour wine and 2 cups chicken broth into roasting pan.
Bake at 325° for 3 hours and 15 minutes to 4 hours or until a meat thermometer inserted into thickest portion of thigh registers 165°, basting every 30 minutes with pan juices. Shield with aluminum foil after 1 1/2 hours to prevent excessive browning, if necessary. Remove from oven, and let stand 30 minutes.
Transfer turkey to a serving platter, reserving 2 1/2 cups pan drippings. Pour reserved drippings through a fine wire-mesh strainer into a bowl, discarding solids.
Melt remaining Béarnaise Butter in a saucepan over medium heat; whisk in flour, and cook, whisking constantly, 1 to 2 minutes or until smooth. Gradually add reserved drippings to saucepan, and bring to a boil, whisking constantly. Reduce heat, and simmer, stirring occasionally, 5 minutes or until thickened. Add up to 1/2 cup remaining chicken broth for desired consistency. Add salt and pepper to taste. Serve turkey with gravy.