Pre-heat the oven to 400°F.
Pat the outside of both turkeys with paper towels until they are relatively dry. Stuff the cavities of both birds with the onions, carrots and celery. Place five to six sprigs of thyme and two bay leaves in each bird. Season the outside of the birds with the grill and poultry seasonings, along with some salt and pepper. Rub the outside of each turkey with the soft butter, then place in a large roasting pan. Tie the ends of the turkey legs together with trussing string.
Transfer the turkeys to the oven and roast until a meat thermometer reads 160°F, about 2 1/2 hours. Remove the turkeys from the oven and let them rest, loosely covered with foil, for at least 20 minutes.