Before making the turkey, two nights prior, bring a stockpot containing all brine ingredients (except for ice water) to a boil. Cover and switch off the heat; let it cool down and place in refrigerator overnight.
About 12-13 hours before time to cook, put the turkey (breast side down) in a brine bag and fill it with brine as well as ice water. Seal the bag while expelling air, twist the extra part of the bag to ensure that the poultry is entirely submerged, and tie it off with twine. Place this entire bag in a cooler full of ice packs for about one hour before you intend to serve.
Drain the turkey from the brine bag and rinse it off. Dry with paper towels before applying spice rub to all parts of the skin, making sure to cover evenly. Tie the wings and legs to the body, as well as the ends of the drumsticks together with twine. Place turkey spine side down into the fryer basket and use twine to secure the turkey in place, running a layer across the top of the turkey and through each hole of the fryer basket. This will help keep it from floating around while cooking.
When it's time for cooking, put the turkey fryer outside on newspaper to catch any dripping grease. Heat the oil as per fryer guidelines and wear heat-resistant gloves. Place the basket into the fryer carefully and cook for the amount of time indicated by your fryer size (ours was 45 minutes).
Once cooked, take out the fryer basket (while still wearing gloves) and let it cool down. Cut off the twine holding it to the basket and transfer it to a roasting pan for further cutting of twines and carving. Serve hot.