In a large pot over high heat, combine the salt, brown sugar, peppercorns and the 1 gallon water. Bring to a boil and continue boiling, stirring to dissolve the salt and sugar, about 3 minutes. Remove from the heat and transfer to a large bowl. Let cool to lukewarm, about 1 hour. Stir ½ gallon of the ice water into the brine.

Place the turkey in the brining bag. Pour in the brine and the remaining 1 gallon ice water. Using the sealing clip, seal the bag securely and refrigerate for 6 to 24 hours. For added stability, place the bag in a pot or on a baking sheet.

Preheat an oven to 425°F.

Remove the turkey from the brine. Rinse the turkey thoroughly with cold water and pat dry with paper towels. Discard the brining bag.

Place the turkey, breast side up, on a rack in a large roasting pan. Brush the turkey with the butter and roast for 30 minutes. Reduce the oven temperature to 350°F and continue roasting, basting occasionally with the pan juices, until an instant-read thermometer inserted into the thickest part of the breast, away from the bone, registers 165°F, and inserted into the thigh registers 175°F, about 2 ½ hours more. If the breast begins to cook too quickly, tent it loosely with aluminum foil. Total roasting time should be about 3 hours.

Transfer the turkey to a carving board, cover loosely with foil and let rest for about 20 minutes before carving. Reserve the pan drippings for the gravy, if desired. Carve the turkey and arrange on a warmed platter. Serve immediately.