For the marinade: combine all of the ingredients except the chicken until evenly combined. Add the chicken, turn to coat, cover, and refrigerate at least 2 hours and up to 6 hours.
When ready to cook, heat the oven to 425 degrees F. Arrange a rack in the upper third of the oven. Nest a cooling rack inside a rimmed baking sheet lined with aluminum foil, set aside.
Combine the cornmeal, cornflakes, cheese, oil, salt, black pepper, and cayenne in a shallow bowl and mix until well combined; set aside. Whisk together the eggs in a shallow bowl until evenly combined; set aside.
To coat the chicken, remove it from the marinade and let any excess drip off. Dip the chicken in the beaten eggs then in the cornflake mixture, turning to coat all over and pressing to help it adhere. Place the chicken pieces on the prepared baking sheet and repeat with remaining chicken. Let the chicken rest on the baking sheet for 15 minutes before baking.
Bake until the coating is golden and crispy, the juices of the chicken run clear when poked, and the internal temperature is 160 degrees F, 40-45 minutes.
Note-you can coat the chicken and return it to the fridge and let it sit for up to 4 hours before cooking. Just let it sit at room temperature for 15 minutes before baking so it cooks more evenly.