Nashville Hot Chicken

In a large bowl, season chicken generously with salt and pepper. Cover with plastic wrap and let chill in fridge 3 hours or up to overnight. Line a large rimmed baking sheet with a metal rack. In a shallow bowl, whisk together milk, eggs, and hot sauce. In another shallow bowl, whisk together flour, paprika, and cayenne. Pat chicken dry, then dredge in flour mixture, then milk mixture, then flour mixture again, and place on wire rack. Repeat until all chicken is breaded.  In a large pot, heat oil until a candy thermometer inserted into pot reads 350°. Working in batches, fry chicken until golden, about 6 to 8 minutes. Scoop out 1/2 cup hot oil, and let remaining oil cool in pot before discarding.  Make spicy oil: In a large heatproof bowl, whisk together cayenne pepper, brown sugar, paprika, garlic powder, chili powder, and salt. Pour in reserved hot frying oil and whisk to combine. Brush over chicken before serving.