Whisk together buttermilk, mustard, salt and pepper, and cayenne in a bowl, and pour into a resealable plastic bag. Add the chicken pieces, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 2 to 8 hours.
When you are ready to cook the chicken, combine the flour, baking powder, garlic powder, and onion powder in the other plastic bag. Shake to mix thoroughly. Transfer one marinated chicken piece at a time into the dry ingredient bag, and shake well to ensure complete coverage. After all chicken pieces are coated, repeat the process by dipping them in the buttermilk marinade and shaking in the dry coating again.
Heat oil in a large frying pan over medium-high heat, making sure not to burn the oil. When oil is hot, fry chicken in batches until golden brown and juices run clear, turning chicken to brown evenly.