Combine the vegetable stock, salt, brown sugar, and peppercorns in a large stockpot over medium-high heat. Stir occasionally to dissolve solids and bring to a boil. Then remove the brine from the heat, cool to room temperature, and refrigerate.
The night before combine the brine, water and ice in a 5-gallon bucket or large heavy duty bag. Place the thawed turkey (innards removed) breast side down into the brine. If necessary, weigh down the bird to ensure it is fully immersed, cover, and refrigerate or set in cool area for 8 to 16 hours, turning the bird once half way through brining.
Preheat the oven to 500 degrees F. Remove the bird from brine and rinse inside and out with cold water. Discard the brine.
Place the bird on roasting rack inside a half sheet pan and pat dry with paper towels.
Stuff. Tuck the wings underneath the bird and coat the skin liberally with canola oil.
Roast the turkey on lowest level of the oven at 500 degrees F for 30 minutes. Reduce the oven temperature to 350 degrees F. A 14 to 16 pound bird should require a total of 2 to 2 1/2 hours of roasting. Let the turkey rest, loosely covered with foil or a large mixing bowl for 15 minutes before carving.
Notes
My 32 pound turkey took 6 hours at 325. I chose 325 F because I knew with the turkey being as large as it was that I may have issues with fat dripping on the bottom of the oven. Because of that I lined the bottom of the oven with foil and changed that foil twice during cooking, every two hours.NOTE about brining a big bird. Instead of a bucket I used a heavy duty bag inside of a cooler. You know, the cooler you fill with food, pop and maybe beer all summer long. I place the bagged bird into the cooler then pour the brine into bag. Secure the bag really well with several rubber bands nice and tight. Cover bagged bird with ice and close the cooler. Check every 5 or 6 hours and drain the cooler if needed and replace the melted ice. Keep the turkey nice and cold until you are ready to rinse it and put it in the oven.