If you have leftover pickle juice, add it and the pork chops to a plastic bag and let them sit for an hour.
Bring pork chops to room temperature and pat dry with a paper towel.
Season pork chops with salt and pepper.
Place flour in a shallow dish. Place eggs in a second shallow dish. Toss bread crumbs in a third shallow dish.
Season all thee with salt and pepper
Dredge pork chops in flour, dip in eggs, and coat both sides well. Coat in bread crumbs.
Place on a wire rack and let sit for 10 minutes before cooking.
Pour 1/4-inch of oil and 1 tbsp butter into a large cast iron pan. Heat over medium-high heat. When hot, add pork chops.
Fry pork chops for about 3 minutes on the first side and 2 to 3 minutes on the second side. Thinner pork chops will need less time to cook. Remove to the wire rack.
You can place them in a 180° oven to keep warm if need be.
To make gravy, drain the oil out of the cast iron pan. Add butter and melt over medium-high heat.
Add flour and cook and stir for 1 minute.
Gradually whisk in the pickle juice, Dijon, hot sauce, and buttermilk one at a time and bring to a boil. Add salt and pepper and simmer for 2 minutes.
Taste for seasoning and serve on the side or over the pork chops.