Special equipment: a turkey fryer
In a stockpot large enough to submerge the turkey, combine the salt, sugar, onions, garlic, thyme, bay leaves, peppercorns, fennel seeds, juniper berries, mustard seeds and 10 cups water. Bring to a simmer, stirring until the salt and sugar have dissolved. Turn off the heat. Add another 15 cups cold water and 9 cups ice, and stir until the ice melts. Place the turkey in the pot and submerge until it fills up with the brine. Cover and refrigerate for 12 to 24 hours.
Remove the turkey from the brine and place on a baking sheet fitted with a cooling rack. Pat the turkey dry with paper towels, then return to refrigerator, uncovered, for up to 12 hours to dry. Let sit at room temperature for 30 minutes before cooking.
Drizzle the peanut oil all over the turkey, rubbing it into the joints and underneath. Then rub the Creole seasoning all over turkey. Place turkey, breast-side up, into a fryer basket, making sure to center the bird. Cook per fryer instructions until the turkey reaches 165 degrees F at the deepest part of the breast, 1 1/2 to 2 hours.
To remove the turkey from the oil, carefully lift the fryer basket using heat-proof gloves. Gently slide turkey out of basket onto cutting board. Loosely cover with foil. Let rest for 30 minutes before carving. Meanwhile, remove the drip pan from fryer and separate the fat from the turkey drippings.
For the gravy: Add 2 tablespoons fat from the turkey dripping to a large saute pan over medium heat. Add the shallots and thyme, and saute until translucent and soft, 3 to 4 minutes. Add 1 teaspoon salt, 1/2 teaspoon pepper, and the sherry, and cook until the liquid is absorbed, scrapping up any bits in the pan. Add the broth and 1/2 cup of the turkey drippings, whisking until combined. In a small bowl, whisk the cornstarch with 1 tablespoon water. Whisk the cornstarch slurry into gravy and cook until thickened, about 1 minute. Taste for seasoning. Serve warm.