A whole 4-pound chicken, cut into 10 pieces (4 breast pieces, 2 drumsticks, 2 thighs, 2 wings), can be used instead of the chicken parts. Skinless chicken pieces are also an acceptable substitute, but the meat will come out slightly drier. If using kosher chicken, do not brine in step 1.
1. Whisk 1 quart cold water, 1/4 cup salt, and sugar together in large bowl until sugar and salt dissolve. Add chicken, cover, and refrigerate for 1 hour. Remove chicken from brine and pat dry with paper towels. Set wire rack in rimmed baking sheet and line plate with triple layer of paper towels.
2. Place 1/2 cup cornstarch in large zipper-lock bag. Beat egg, baking powder, and baking soda together in medium bowl; stir in buttermilk (mixture will bubble and foam). Whisk remaining 1/2 cup cornstarch, cornmeal, garlic powder, paprika, cayenne, and 1 teaspoon salt together in shallow dish.
3. Working with half of chicken at a time, place chicken in bag of cornstarch, seal bag, and shake bag to coat chicken. Using tongs, remove chicken pieces from bag, shaking off excess cornstarch, dip in buttermilk mixture, then coat with cornmeal mixture, pressing gently to adhere. Place dredged chicken on prepared wire rack, skin side up. Cover loosely with plastic wrap and let sit 30 minutes.
4. Meanwhile, add oil to large Dutch oven until it measures about 2 inches deep, and heat over medium-high heat to 350 degrees. Adjust oven rack to middle position and heat oven to 200 degrees. Carefully place half of chicken in pot, skin side down, cover, and fry, stirring occasionally to prevent pieces from sticking together, until deep golden brown, 7 to 11 minutes. Adjust burner, if necessary, to maintain oil temperature between 300 and 325 degrees. (After 4 minutes, check chicken pieces for even browning and rearrange if some pieces are browning faster than others.) Turn chicken pieces over and continue to cook until breast pieces register 160 degrees and drumsticks and/or thighs register 175 degrees, 6 to 8 minutes. (Smaller pieces may cook faster than larger pieces. Remove pieces from pot as they reach correct temperature.) Drain chicken briefly on paper towel–lined plate, then transfer to clean wire rack set in rimmed baking sheet and keep warm in oven.
5. Return oil to 350 degrees and repeat with remaining chicken. Serve.