Season both sides of the pork chops with ½ teaspoon kosher salt and ½ teaspoon black pepper.
Add 1 tablespoon olive oil to a large heavy bottomed skillet or saute pan, and heat over MEDIUM-HIGH heat. Add the pork chops to the pan and cook for 3 to 4 minutes per side, or until the pork chops are well browned and partially cooked through (they’ll finish cooking in the sauce). Transfer the pork chops to a plate and set aside.
In a measuring cup or small mixing bowl, whisk together the chicken broth, mustard, and vinegar and set aside.
Add the remaining 1 tablespoon oil to the pan. Add the apples and onions and cook, stirring occasionally, for 4 minutes, or until the onions are tender. Season with the remaining ½ teaspoon salt, ¼ teaspoon pepper, sage, rosemary, and thyme and stir to combine.
Pour the broth mixture into the pan and using a wooden spoon, scrape up any brown bits from the bottom of the pan. Add the butter and stir until melted.
Return the pork chops back to the pan along with any accumulated juices, nestling them down in between the apples and onions. Cook 3 to 4 minutes more (sauce should be bubbling), or until the pork chops have reached an internal temperature of 145 degrees F and the liquid has reduced by about half.
Serve the pork chops with the apples and onions and spoon the pan sauce over the top.