In a large measuring cup or pitcher, combine ¼ cup salt and 2 cups hot tap water. Stir until dissolved. Add 2 cups cold tap water and stir to combine.
Add chicken pieces to a large resealable plastic bag. Pour brine into bag and seal. Transfer to refrigerator, 8-12 hours.
Fill a large dutch oven or cast iron pot with enough oil to reach a depth of 4 inches. Over medium-high, heat oil to 350 degrees on a candy or deep fry thermometer. Place a wire rack over a sheet pan and place next to stove.
In a deep pie plate or cake pan, combine flour, cayenne, paprika, celery seed, 1 tablespoon plus 1 teaspoon salt, and 1 tablespoon plus 1 teaspoon black pepper. Whisk to combine. Remove a piece of chicken from brine. Without shaking off too much liquid, dip directly into flour mixture. Using both hands, adhere flour mixture to chicken, using a pinching motion with your fingers to create a rough, shaggy texture with the flour. The more you pinch to create this shaggy effect, the more crunchy and textured the fried chicken will be. Place on a baking sheet and repeat with remaining pieces.
Carefully lower 3-4 pieces of chicken into the hot oil. Do not overcrowd. Fry, flipping occasionally until chicken pieces are deeply golden and read 160 degrees on an instant-read thermometer, about 10-12 minutes. Remove with a slotted spoon to the prepared rack, and repeat with remaining pieces, adjusting the flame to maintain 350 degrees.