My first preference will always be a deep fry. You drop the chicken pieces into the deep fat fryer and they are immersed totally so that the entire batter is exposed to the hot oil instead of just one side. However, here is a recipe based on a shallow fry until golden in a cast iron pan and then finishing off in the oven.
I have become a fan of skinless chicken for frying.
2 cups buttermilk
2 large eggs, beten
3 tsp. Kosher salt (or to taste...I prefer to undersalt as one can always add more salt at the table) divided into a 1 tsp. and a 2 tsp. portion
3 garlic cloves crushed
2 1/2 tsp. black pepper also divided into two equal portions
2 lbs. bone-in skinless chicken thighs and 2 lbs. boneless, skinless chicken breasts (each one to be cut in half)
2 cups of vegetable oil for frying ( I don't like canola oil because it smells like frying fish)
3 cups all purpose flour
2 tbsp. cornstarch
Whisk together the buttermilk, eggs, garlic, 1 1/4 tsp. Kosher salt, 1 tsp black pepper in a large bowl and then, with the chicken pieces placed into a large plastic freezer bag, add the liquid mixture. Seal the bag and refrigerate for 8 to 24 hours.
Remove the chicken pieces and allow to drain well. Meanwhile, whisk the flour, cornstarch, the remaining salt and pepper in a bowl and dip/dredge the chicken pieces in the dry mix. Or, place the dry mix in a paper bag, adding the pieces of drained chicken and shaking to coat. Place the pieces on a pan, or piece of aluminum foil. Let them "dry out" for around 15 minutes or so.
Fry the chicken in batches in a cast iron pan. Heat should be medium high. In all probability, if you checked it with a thermometer, it would be around 350 F. Meanwhile also heat the oven to 425 F.
Now, the trick is, with turning them once or twice, to develop the classic "golden brown" color. Some people say 3 minutes per side. Use your judgement.
You are going to finish the pieces in the oven.
Now, these days, chickens have gotten huge and you are going to want to be sure that they are cooked all the way through. Check the pieces after they have been in the oven for 10 minutes. They may be done at that time.