Fill large saucepan with 1 gallon cold water. Place saucepan over medium-high heat and bring water to boil.
When water begins to boil, add salt, brown sugar, whole peppercorns, rosemary, thyme, and bay leaves. Remove saucepan from heat and stir ingredients together until salt and sugar have dissolved completely. Set saucepan aside.
Fill large container with remaining 2 gallons of very cold water. Pour brine mixture into cold water and stir quickly to incorporate, then let mixture sit until water has cooled completely. Add ice if needed to bring water below room temperature.
When water is cool, place turkey breast-side down in container with brine. Turkey must be completely submerged in brine.
Cover container and let turkey sit in brine at room temperature 3 to 4 hours. If preferred, refrigerate turkey in brine 6 to 8 hours instead. Be careful not to over-brine turkey.
After turkey has sat in brine for desired length of time, remove turkey from container and discard brine. Pat turkey completely dry with paper towels, then cook turkey immediately using desired method, or place turkey in roasting pan and refrigerate overnight to air dry.