A day before your cook, put all the brine ingredients, except for ice, into a pot and boil for 10 minutes. Pour liquid over ice into the brining bucket. Once the liquid is cool place the turkey into the bucket, making sure the turkey is completely submerged. Cover tightly, and put into the fridge and brine for 8-24 hours. When ready to cook, remove the turkey from the brine and rinse thoroughly.
Set the EGG for indirect cooking with the convEGGtor at 350°F/204°C.
Pat the turkey dry and coat with oil, season with salt and Big Green Egg Savory Pecan Seasoning.
Place half of the onion, one whole head of garlic, half the orange, half the lemon, and two sprigs of each herb inside the cavity of the turkey. Fold the wings back behind the turkey so that they cook evenly. Put the turkey on the roasting rack and place into the drip pan. Add the remaining garlic, onion, orange, lemon and herbs around the turkey in the drip pan.
Place on the EGG and cook 3-4 hours or until the internal temperature is 165°F (white meat) and 185°F (dark meat). During the cook, cover the turkey with aluminum foil once the skin has the desired color and texture.
Remove from the EGG, let rest for 15 minutes. Carve and enjoy!