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To make the batter:
Whisk the egg well in a stainless steel bowl and add the peanut oil and 2 1/2 cups water. In a separate bowl, combine all the remaining batter ingredients, then add the dry mixture to the egg mixture, whisking slowly so the batter doesn't clump.
While the oil is heating, remove the chicken from the brine and place in a colander in the sink. Once the chicken has drained, pat it dry with paper towels (a critical step) and season with salt and pepper. Dip the chicken in the batter and place it (carefully) in the hot oil. Adjust the heat, as the chicken will bring the oil temperature down dramatically-you want it back up to just above 350degreesF. Turn the chicken regularly using tongs to prevent burning. After 8 or 9 minutes, remove a piece, prick it to the bone with a fork, and mash it. If the juices run clear, it's done. Continue cooking if necessary.
To make the pickle-garlic relish:
Finely chop and combine all the relish ingredients.
Serve with the chicken. Cover any leftovers with a dishtowel and leave out at room temperature (or in the fridge, if you must, although my grandmother never did). This keeps it crisp.