Season the chicken with 3/4 tsp salt and refrigerate it in 3/4 cup buttermilk for at least 30 minutes and up to 4 hours.
Heat the peanut oil in a heavy pot to 350°F and set a wire rack over a sheet pan.
Whisk the egg into the remaining 1/4 cup buttermilk in a small bowl.
Combine the flour, remaining 1/2 tsp salt, paprika, garlic powder, black pepper and cayenne in a wide dish, then drizzle in the egg mixture and rub it into small clumps.
Lift each tender from the marinade, let the excess drip and press it firmly into the clumpy flour mixture.
Fry four or five tenders at a time, turning once, until deep golden and 165°F inside, 4 to 6 minutes total.
Drain on the rack, let the oil return to 350°F between batches and serve while the ridges are crisp.
