Preheat oven to 325 degrees F. Remove neck and giblets from turkey; discard. Rinse body cavity of turkey; pat dry with paper towels.
To prepare rub, in a blender or food processor combine arugula, basil, cheese, walnuts, olive oil, garlic, salt, and pepper. Cover and blend or process with several on/off turns until a paste forms, stopping several times to scrape the side of the blender or food processor.
To apply rub, slip your fingers between the skin and meat on the breast of the turkey to loosen skin. Lift skin and spread the rub under the skin from front to back of the turkey. If desired, rub any remaining mixture on the outside skin of the turkey or rub with vegetable oil. Skewer neck skin to back. Tie drumsticks together or to the tail with clean 100-percent-cotton kitchen string. Twist wing tips under back. Place turkey, breast side up, on a rack in a shallow roasting pan.
Insert an oven-going meat thermometer into the center of an inside thigh muscle. Thermometer should not touch bone. Cover turkey loosely with foil. Roast turkey for 2 1/2 hours. Remove foil; cut band of skin or kitchen string between drumsticks so thighs cook evenly. Continue roasting for 30 to 75 minutes more or until the meat thermometer registers 180 degrees F and turkey is no longer pink (the juices should run clear and drumsticks should move easily in their sockets). Remove turkey from oven. Cover with foil; let stand for 15 to 20 minutes before carving. Transfer turkey to a cutting board. Carve turkey.