To prepare turkey, trim excess fat. Starting at neck cavity, loosen skin from breast by inserting fingers, gently pushing between skin and meat.
Combine 2 tablespoons tarragon and next 6 ingredients (through garlic), stirring well. Rub tarragon mixture under loosened skin and over breast meat. Place turkey, breast side up, on a wire rack coated with cooking spray. Place rack in a roasting pan. Pour 1 1/2 cups water into pan. Bake at 350° for 1 hour. Baste turkey with pan juices. Bake an additional 30 minutes or until a thermometer registers 165°. Remove turkey from oven. Loosely cover with foil; let stand 20 minutes. Remove skin from turkey; discard. Thinly slice turkey.
To prepare mayonnaise, combine mayonnaise and the remaining ingredients, stirring well. Serve with turkey.