Pat the pork chops dry with paper towels and season both sides generously with salt and pepperāthis is key for getting a good sear!
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until the butter is melted and the pan is nice and hot.
Add the pork chops to the skillet and cook for 4-5 minutes per side until they're golden brown and cooked through (internal temperature should reach 145°F). Remove them from the pan and set aside on a plate.
In the same skillet (don't clean itāall that flavor stays!), add the remaining 2 tablespoons of butter and let it melt over medium heat.
Toss in the apple slices and cook for about 3-4 minutes until they start to soften and caramelize slightly.
Sprinkle the brown sugar, cinnamon, and nutmeg over the apples, stirring everything together so the apples get coated in those warm fall spices.
Pour in the apple cider, chicken broth, and honey, then add the thyme. Let this simmer for 5-6 minutes, stirring occasionally, until the sauce thickens up and the apples are tender.
Return the pork chops to the skillet, nestling them into the apple mixture, and spoon some of that gorgeous sauce over the top. Let everything warm through for 2-3 minutes.
Serve the pork chops with plenty of apples and sauce spooned over the top, and garnish with fresh sage if you want to make it extra pretty!