In a mixing bowl, add the eggs and buttermilk. Use a fork and whip to combine. Add all the chicken pieces and toss to coat with the egg and buttermilk mixture. Cover and refrigerate for 2 to 4 hours. Refrigerating can be omitted but is recommended if time permits.
In a gallon-size Ziplock bag, add the flour, salt, black pepper, and paprika. Shake to combine. Add a few pieces at a time and shake to coat. Place the coated pieces on a plate. Once all the pieces are coated, return them to the bag, shake, and coat once more.
Add the oil to a large skillet. Turn to medium-high heat and allow the oil to get hot. Don't let the oil get to the smoking point before adding the chicken. Sprinkle a pinch of flour into the oil. When the oil sizzles, it’s ready for the chicken.
Add chicken pieces to the oil and turn the burner to medium heat. Don’t overcrowd the skillet. I usually cook the breasts and thighs first. Always keep an eye on the chicken while frying. Use tongs or a fork to turn the pieces over when they're golden on one side.
Remove the chicken pieces when they are golden brown on both sides and cooked through. Test the chicken by piercing it with a fork; if the juices run clear, it's done. Place the cooked chicken on a baking sheet lined with paper towels. Adding more oil may be needed before adding additional pieces. Make sure the oil is once again hot and tested with a pinch of flour before adding more chicken.
Continue to add chicken to the oil until all the pieces are done and juices run clear. Allow to cool slightly before serving.
