Drain the pickling liquid into a medium bowl, reserving the pickles separately. Add the chicken into the pickling liquid and cover. Refrigerate for 4 to 6 hours.
To make the sauce, combine the mayonnaise, BBQ sauce honey and yellow mustard.
Combine the flour, 1 teaspoon salt and a pinch of pepper in a medium bowl. Whisk together the eggs, 1 teaspoon salt and a pinch of pepper in a separate medium bowl.
In a large heavy-bottomed saucepan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 375 degrees F. (If you don't have a thermometer, a cube of bread will brown in about 3 minutes.)
Remove the chicken from the brine. Discard the brine. Dredge the chicken in the flour, then in the egg and then back in the flour. Fry the chicken until brown and crisp, 6 to 8 minutes. Remove onto a paper-towel-lined plate and season with a pinch of salt.
Build the sandwich with the buns (toasted with butter, if desired), chicken, a drizzle of sauce and pickles.
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