Special equipment: a brining bag (optional) and an electric turkey deep-fryer
Three days before roasting the turkey, make the brine.
For the brine: In a large pot on medium-high heat, add 6 quarts (24 cups) water and the salt, peppercorns, sage, thyme and lemon. Bring to a boil, lower to a simmer and simmer until the salt is dissolved and the water is fragrant. Turn off the heat and let cool.
Put the turkey in a brining bag, large plastic bag or a bowl large enough to fit it with still more space to give. Pour in the cooled brining liquid and seal or cover. If there's not enough room for all of the liquid in the brine, be sure to at least include the herbs, lemon and peppercorns in with the turkey for brining. Refrigerate for 3 days.
When ready to cook, remove the turkey from the refrigerator and discard all of the brining liquid and solids. Pat the turkey dry with paper towels.
For the rub: In a medium bowl, mix the pumpkin pie spice, paprika, salt, cumin and pepper. Rub the mixture on all sides of the turkey and drizzle lightly with olive oil. Leave at room temperature for 2 hours. (If you have an extra day in your planning, leave it in the refrigerator overnight uncovered. This will help dry the skin more, then when ready to fry, remove from the refrigerator and let rest at room temperature for 2 hours.)
Fill the fryer with vegetable or canola oil and heat to 350 degrees F according to the manufacturer's instructions (see Cook's Note).
Cook the bird for approximately 3 minutes per pound and then add an additional 5 minutes onto the cooking time. A 15-pound bird will take about 50 minutes. (Check the cooking times on your fryer; cook according to instructions and fry for the correct time according to weight.) Remove to a paper towel-lined platter and allow to rest for at least 30 minutes or up to 1 hour so the juices can redistribute, then carve.
To measure the amount of oil needed to fry the turkey, put the turkey in the fryer, add water to top of turkey, and mark the water line with a crayon or marker. Remove the turkey and the water line will indicate how much oil will be needed to fry your turkey. Having too much oil can cause a fire. The pot should not be more than 3/4 full or the oil could overflow when the turkey is added. Dry the fryer before adding the oil.
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