To ensure a crispy, golden coating and well-cooked meat, keep an eye on the temperature of the oil; it needs to come back up to 350 degrees before adding the second batch of chicken.
Combine 1 cup water with remaining brining ingredients in small saucepan over medium heat, stirring just until salt and sugar are dissolved. Remove from heat and cool to room temperature. Combine brine mixture with remaining cold water in a large bowl or deep baking dish. Add chicken to bowl, making sure chicken is covered with the brining liquid. Store in fridge at least 8 hours and up to 24 hours.
Remove chicken from brining liquid and pat dry. Combine flour, cornmeal, salt, and red pepper flakes in a shallow dish. Whisk eggs in another shallow dish. Coat chicken in flour mixture, then eggs, and again in flour mixture. Transfer to a rimmed baking sheet lined with a cooling rack.
Heat oil to 350 degrees in a large pot. Working in 2 batches, fry chicken for 15 minutes, turning once, until chicken is deep golden brown. Transfer to a paper towel-lined plate to drain. Serve hot or cold.