Whisk the buttermilk, salt, and pepper together, submerge the chicken thighs completely, cover, and refrigerate for at least 2 hours or overnight.
Toss the shredded cabbage and grated carrot together, whisk the mayo, vinegar, sugar, salt, and pepper, pour over the vegetables, toss to coat, and refrigerate until needed.
Whisk the flour, garlic powder, paprika, and salt together in a shallow dish. Remove the chicken from the brine, let the excess drip off, and press firmly into the flour until fully coated. Rest on a wire rack for 10 minutes.
Heat 2 inches of neutral oil to 325°F (160°C) and fry the chicken in batches for 6 to 8 minutes per side until deep golden brown and the internal temperature reaches 165°F (74°C). Transfer to a wire rack and reserve half a cup of the hot oil.
Whisk the cayenne, brown sugar, and smoked paprika into the reserved hot oil until a smooth glossy glaze forms.
Brush the glaze generously over both sides of the hot chicken.
Toast the buns in a buttered pan until golden, spread mayo on both halves, stack the glazed chicken, a handful of slaw, and dill pickles, and serve immediately.