Combine chicken stock, salt, brown sugar, onion, pepper flakes, cinnamon sticks, peppercorns, allspice berries, and candied ginger in a large stockpot over medium-high heat; bring to a boil. Stir until sugar and salt have dissolved, 3 to 5 minutes. Remove from the heat, cool to room temperature, and refrigerate brine until thoroughly chilled.
Combine brine and ice water in a clean, food-grade, 5-gallon bucket. Place turkey in the brine, breast-side down. Cover and refrigerate (or set in a cool area like a basement) for 6 hours, turning turkey once halfway through.
Set an oven rack to the lowest level and preheat the oven to 500 degrees F (260 degrees C). Place a roasting rack inside a wide, low pan.
Remove turkey from brine and rinse inside and out with cold water. Discard brine. Place turkey on the roasting rack and pat dry with paper towels. Tuck back the wings and rub butter liberally over the entire bird.
Roast turkey in the preheated oven for 30 minutes. Remove from the oven, insert a probe thermometer into the thickest part of the breast, and cover the breast with a double layer of aluminum foil.
Return to the oven, reduce temperature to 350 degrees F (175 degrees C), and cook until no longer pink at the bone and the juices run clear, 3 to 3 1/2 hours longer. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read 165 degrees F (74 degrees C). Remove from the oven, keep loosely covered, and allow to rest in a warm area for 15 minutes before slicing.