Preheat the oven to 350ºF. In a small bowl, combine the brown sugar, cayenne pepper, garlic powder, paprika, salt, and black pepper.
Remove the pork chops from their package and rub the seasoning mixture over all sides of each chop. The moisture from the meat will help the seasoning to adhere to the surface.
Heat olive oil in a large, oven-safe skillet over a medium flame. When the oil begins to shimmer, add the pork chops. Cook the chops for about 5 minutes on each side, until nicely browned.
If your chops are greater than one-inch thick, transfer the skillet to the preheated oven for another 5-10 minutes to finish cooking. Test the chops with a meat thermometer to make sure the internal temperature has reached 145ºF. Cook longer if needed.
Dredge the chops through the thick sauce in the bottom of the pan just before serving.
In a large skillet or saucepan, melt butter over medium heat; add apples. Cook, stirring constantly, until apples are almost tender, about 6 to 7 minutes.
Dissolve cornstarch in water; add to skillet. Stir in brown sugar and cinnamon. Boil for 2 minutes, stirring occasionally. Remove from heat and serve warm.