In a large pot, dissolve 1 cup of kosher salt and 1 cup of brown sugar in 1 gallon of water over medium-high heat. Add 2 bay leaves, 2 sprigs of thyme, and 2 sprigs of rosemary. Remove from heat and let cool to room temperature.
Place the turkey in a large brining bag and pour the cooled brine over the turkey. Seal the bag and refrigerate for 24 hours.
Preheat the oven to 3500F. Remove the turkey from the brine and pat dry with paper towels.
In a small bowl, mix the softened butter with chopped parsley, sage, and thyme. Season with salt and pepper.
Carefully separate the turkey skin from the breast and legs with your fingers. Rub the herb butter under the skin, making sure to cover as much of the meat as possible.
Season the outside of the turkey with salt and pepper. Tie the legs together with kitchen twine and tuck the wings under the body.
Place the turkey in a roasting pan and roast for 15-20 minutes per pound, or until a meat thermometer inserted into the thickest part of the thigh registers 1650F.
Let the turkey rest for at least 20 minutes before carving.