Combine 1 cup of water, 2 tablespoons pepper, and thyme sprigs in a small saucepan. Bring to a boil, and remove from heat. Pour into a large bowl; cool to room temperature. Add remaining 6 cups water, salt, honey, and sugar, stirring until salt and sugar dissolve. Pour salt mixture into a 2-gallon zip-top plastic bag. Add ice and turkey; seal. Refrigerate 24 hours, turning the bag occasionally. Remove turkey from bag, and discard brine. Pat turkey dry with paper towels.
Rub turkey with oil. Combine 1 tablespoon pepper and chopped thyme; rub over turkey.
Preheat oven to 400°.
Place the turkey on a roasting pan coated with cooking spray. Bake at 400° for 1 hour or until thermometer inserted into thickest portion of the breast registers 180°. Place turkey on a platter. Cover with foil; let stand 15 minutes. Garnish with thyme sprigs, if desired.