Dissolve salt and sugar for the brine in hot water in a large bowl or container. Add the ice and stir to cool the mixture. Prepare the chicken pieces by removing skin and piercing with a meat knife. Add to brine and refrigerate for 1 1/2 - 2 hours.
Preheat the oven to 400 degrees. Coat a 4-quart Pyrex baking dish with nonstick cooking spray.
Combine flour, pepper, salt, and paprika in a large, heavy bag. Remove chicken pieces from brine and pat dry. Place a few pieces of chicken in the flour mixture and toss to coat. Shake off excess flour and place on a rack. Let stand for 10 minutes.
Beat egg whites to soft peaks.
Add buttermilk and stir gently. Dip floured chicken pieces in egg white mixture and place back into the seasoned flour bag. Shake. Gently transfer to a cooking rack. Repeat with remaining chicken.
Heat oil in the prepared Pyrex dish by placing in the oven for 5 minutes.
Set prepared chicken meaty side down into the hot dish. Roast for 30 minutes. Remove dish from oven and carefully turn chicken pieces over. Return to oven and roast 20 minutes more. Let chicken set about 15 minutes before serving.