Pat the pork chops completely dry on both sides with paper towels. Season each chop all over with the kosher salt, black pepper, and dried thyme.
Let the seasoned chops sit at room temperature for about 15 minutes while you slice the apples and onion.
Core the apples and slice them into 1/2-inch (1.25 cm) wedges, leaving the skin on. Halve the onion and slice it thinly into half-moons. Mince the garlic and chop the sage.
Heat the olive oil in your large skillet over medium-high heat until it shimmers. Add the chops and sear without moving them for 3 to 4 minutes, until a deep golden crust forms.
Flip once with tongs and sear the second side for another 3 minutes. Transfer the chops to a plate and tent loosely with foil; the pork will not be fully cooked yet.
Lower the heat to medium and add the butter to the same skillet. Add the sliced onion and cook for 4 to 5 minutes, stirring often, until it softens and turns golden.
Add the apple wedges and cook for another 4 minutes, until they start to caramelize at the edges but still hold their shape. Stir in the minced garlic and sage and cook for 30 seconds, just until fragrant.
Pour in the apple cider and chicken broth, scraping the bottom of the pan with a wooden spoon to lift all the browned bits. Stir in the Dijon mustard, maple syrup, and apple cider vinegar.
Bring the sauce to a gentle simmer and let it cook for 2 to 3 minutes to blend the flavors. If you want a thicker sauce, stir in the cornstarch slurry now and simmer for another minute until it coats the back of a spoon.
Nestle the seared chops back into the skillet, spooning some apples and sauce over the top. Simmer gently for 4 to 6 minutes, until the pork reaches 145°F (63°C) on an instant-read thermometer.
Turn off the heat and let everything rest in the pan for 3 minutes so the juices settle. Spoon the apples and sauce generously over each chop and serve warm.