Season the pork chops. Season both sides of the pork chops generously with freshly ground black pepper.
Sear the pork chops. Heat 1 tablespoon of butter and 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the pork chops and sear for 3–5 minutes per side (depending on size), until browned and mostly cooked but not completely done. Remove the pork chops from the skillet and set aside.
Cook the onion. Reduce the heat to medium. Add the remaining tablespoon of butter and olive oil to the skillet. Add the sliced onion and season with salt and pepper. Sauté for 6–8 minutes, stirring occasionally, until the onion is soft and beginning to caramelize.
Add the apples and herbs. Add the sliced apples, sage, and rosemary. Cook for 1 - 2 minutes, just until the apples just begin to soften. Don't overcook here!
Make the sauce. Pour in the chicken broth and whisk in the Dijon mustard. Scrape the browned bits from the bottom of the skillet as the broth comes to a simmer.
Finish the pork chops. Return the pork chops and any juices from the plate to the skillet. Cook for another 4–6 minutes, turning the pork chops once, until they are fully cooked and the sauce has reduced slightly.
Serve. Spoon the apples, onions, and Dijon pan sauce over the pork chops and serve warm. I recommend serving with mashed potatoes, roasted potatoes, or crusty sourdough to soak up the sauce.