In a small bowl, stir together the mustards, honey, lemon juice, and paprika. Set aside. Season both sides of the pork chops with salt and pepper.
In a cast iron pan over medium high, heat the oil until it is shimmering. Add in the butter and then place the pork chops into the pan. Cook for 4-5 minutes or until the pork is golden brown and easily releases from the pan. Flip and repeat on the other side.
Transfer the pork to a plate and drain off any excess oil. Reduce the heat to medium low and pour the honey mustard sauce into the pan. Bring to a simmer and return the cooked pork chops to the sauce.
Let cook for another 1-2 minutes and serve with a generous serving of sauce.
If you have the time, let the pork chops come to room temperature before cooking. This prevents sticking and cuts down on how much oil you need.
Before cooking the meat side, get a crispy fat cap by cooking it first. Do this by placing the pork upright against the side of the pan until crispy. You may need to use tongs to help steady them. This not only renders the fat for more flavorful cooking but also gets the whole pork chop crispy.
Cook the pork chops to an internal temperature of 145°F. This should have a little blush of pink and still be very moist.
To keep the top of the pork chops from drying out, flip them in the sauce before leaving them to simmer.