Note: Start brining the chicken one to two days before you plan to serve it.
Brine the chicken: Combine dry brine ingredients and toss with chicken thighs to coat. Allow chicken to brine in refrigerator for 24 to 48 hours.
Make the deviled egg sauce: Halve eggs and remove yolks. Place warm yolks and ¼ of whites in a food processor and add mayonnaise, buttermilk, mustard, and salt. Blend until very smooth, about 2 to 3 minutes. If under-seasoned, add a splash of apple cider vinegar instead of more salt. Refrigerate until ready to assemble biscuits.
Make the spicy mayo: Combine ingredients until smooth. Refrigerate until ready to assemble biscuits.
Dredge and fry the chicken: Add 1 inch of oil to a cast-iron skillet over medium-high heat. Preheat oven to 350 degrees. Combine dredge ingredients and sift mixture to remove any lumps. In a separate bowl, whisk buttermilk and eggs until combined. Dip chicken thighs into buttermilk to coat, shake off extra liquid, then into the flour mixture, patting down gently to coat evenly and completely.
When oil reaches 350 degrees, slowly add breaded chicken. Fry on each side for 4 to 5 minutes or until internal temperature reaches 165 degrees. Thicker thighs can be finished in the oven on a rack over a sheet pan for 6 to 8 minutes.
To serve: Build each biscuit with spicy mayo, fried chicken, pickles, and deviled egg sauce. Serve immediately.