2 teaspoons fine sea salt
3 teaspoons freshly ground black pepper
For the brine: Heat the water, thyme, garlic, peppercorns, bay leaves, salt and brown sugar in a large saucepan over medium-high heat, stirring frequently, until the salt and sugar dissolve. Transfer to a clean 5-gallon bucket. Add enough ice to total 3 gallons of liquid, and mix until incorporated. Add the turkey to the bucket and transfer to the refrigerator for at least 12 hours. (Alternatively, place the turkey in a large brining bag and fill with enough of the brine to cover the turkey; seal the bag and refrigerate. Or place the bird and brine in a cooler, cover and add ice bags periodically to keep the temperature of the brine below 40 degrees.)
For the turkey: Preheat the oven to 425 degrees. Have ready a large roasting pan with a rack.
Remove the turkey from the brining liquid and use paper towels to pat it as dry as possible, inside and out. Rub the turkey with the butter all over, including the cavity, and sprinkle with the salt and pepper. Fold the wingtips underneath the turkey.
Place the turkey in the roasting pan, breast side up. Tie the legs together with kitchen twine and fold the neck flap under.
Roast the turkey for 1 hour to brown it, then reduce the temperature to 325 degrees and cook for 90 minutes to 2 hours or until a thermometer inserted in the thickest part of the thigh registers 165 degrees.