1. Submerge the chicken thighs in buttermilk mixed with salt and let them marinate for a couple hours, or preferably, overnight in the fridge.
2. In a bowl, mix together the mayonnaise, hot sauce, lemon zest, lemon juice, grated garlic, and salt and pepper. Adjust seasoning to taste and set aside.
3. Toss the red and green cabbage and bell peppers with the 1/4 cup of salt in a strainer. Let it sit for about 30 minutes to sweat out the moisture. Rinse thoroughly, squeeze out excess liquid, and then toss with lemon zest, lemon juice, apple cider vinegar, and salt and pepper. Set aside.
4. In one dish, combine the flour, paprika, garlic powder, onion powder, cayenne, salt, and pepper. In another dish, beat the eggs and add a couple tablespoons of the buttermilk marinade.
5. Dredge each marinated chicken thigh in the flour mixture, then into the egg mixture, and back into the flour for a double dredge. Fry first at 300°F until a light golden crust has formed (5-7 minutes), let them rest. Right before serving, finish frying at 350°F until rich brown and crispy (2-3 minutes). Season immediately after frying.
6. Butter and toast the brioche buns. Spread the spicy aioli on both sides. Place a piece of fried chicken on the bottom bun, add more aioli if you like, top with pickles, and then a heap of the lemony coleslaw. Cap it with the top bun and enjoy!