Remove the pork chops from the refrigerator 30 minutes before cooking and allow to come to room temperature. Pat them dry and season both sides generously with sea salt and black pepper.
Heat the olive oil in a large, heavy skillet over medium high heat until shimmering. Place the pork chops in the skillet and sear for about 4-5 minutes per side until well browned. Transfer the pork chops to a plate and cover to keep warm.
Add the mushrooms to the skillet and cook, undisturbed, until they release their liquid and start to turn golden brown, about 5 minutes.
Stir in the shallot and cook until tender, about 2-3 minutes.
Pour in the chicken stock to deglaze the pan. Scrape up any brown bits of the bottom of the skillet with a spoon. Stir in the mustard, rosemary and thyme and bring to a boil. Reduce the heat to medium-low and simmer until the liquid has reduced by half, about 5 minutes.
Add the figs to the skillet and continue simmering until they have completely softened and the sauce has thickened, about 4-5 minutes.
Swirl the butter or ghee into the skillet, then nestle the pork chops back in along with any juices that have accumulated on the plate. Cook until the pork chops are completely cooked through and reach an internal temperature of 145°F, about 2-3 minutes.