Generously season pork chops with Kosher salt and black pepper.
In a shallow bowl, combine almond flour and arrowroot.
Very lightly coat the pork chops in the almond flour and arrowroot mixture. Adding too much will result in a coating that is overly thick and falls off of the pork chops. These need just a small amount!
Heat avocado oil and 2 tablespoons of butter in a large skillet over medium heat.
Add the pork chops, leaving space around each pork chop to allow for even browning. If your skillet isn’t large, cook 2 pork chops at a time. Allow pork chops to cook for about 10 minutes, or until deeply golden brown, and then flip to cook the other side for another 10 minutes. The internal temperature should reach 135º F. If your pork chops are thick, use a meat thermometer to ensure they are cooked well. Remove browned pork chops from the skillet.
Add shallots, and saute for about 5 minutes to soften.
Add the chicken broth, and allow to simmer until the liquid is reduced by half.
To the broth, add the lemon juice, lemon zest, and additional 2 tablespoons of butter.
Return the pork chops to the pan, and sprinkle with capers. Spoon the sauce over the top of each pork chop, allowing the sauce to soak in to the coating on the pork chops. Serve garnished with Italian parsley.