1. Preheat oven to 350°. Combine first 3 ingredients.
2. Remove giblets and neck from turkey; pat turkey dry with paper towels. Loosen and lift skin from turkey breast with fingers without totally detaching skin; rub butter mixture underneath skin. Carefully replace skin; secure skin at both ends using wooden picks to prevent skin from shrinking.
3. Sprinkle 2 Tbsp. Paprika-Brown Sugar Rub inside cavity. Place apples inside cavity. Tie ends of legs together with string; tuck wingtips under. Place turkey, breast side up, on a rack in a roasting pan. Rub 6 Tbsp. Paprika-Brown Sugar Rub over outside of turkey. Pour chicken broth into roasting pan.
4. Bake turkey at 350°, on lowest oven rack, 2 to 2 1/2 hours or until skin is well browned and a meat thermometer inserted into thickest portion of thigh registers 170°, shielding with aluminum foil during last hour of cooking to prevent excessive browning, if necessary. (Do not baste.) Transfer turkey to a serving platter, reserving drippings in roasting pan. Let turkey stand 20 minutes before carving.
5. Meanwhile, pour pan drippings through a fine wire-mesh strainer into a 4-cup glass measuring cup. Let stand 10 minutes. Skim fat from surface of drippings. (Add chicken broth, if needed, to equal 3 cups.)
6. Melt 3 Tbsp. butter over medium heat in a medium saucepan. Whisk in flour, and cook, whisking constantly, 3 to 4 minutes or until golden. Whisk in 3 cups drippings, and bring to a boil over medium-high heat. Reduce heat to low, and simmer 5 minutes, whisking occasionally. Serve with turkey. Garnish, if desired.