Cut and core the apples. Cut apples into same size cubes.
In a medium sized sauce pan, melt the butter over medium-high heat. Add the apples and sauté for a few minutes, until heated all the way through. Add both brown sugars and spices. Once the apples are well coated with the sugars and spices then add in the apple cider vinegar and dark rum. Simmer for a few minutes while stirring.
While you are simmering the glaze, season the pork chops with salt, pepper and thyme.
Add the chops to the pan. Scoop up some of the sauce and pour it over the chops as they cook thoroughly.
For the glaze- In a medium saucepan, combine all ingredients. Stir to blend and bring to a simmer over medium heat. Cook and reduce for 4-5 minutes to allow all ingredients to blend.
For the apples- Preheat the oven to 375°F. Core each of the apples and place in a large baking dish. Put a cinnamon stick inside the cavity of each apple. Pour the glaze over the apples and top each with pieces of butter.
Pour the apple juice in the bottom of the baking dish and place dish in the center of the oven.
Cook the apples, basting them from time to time, until they are tender but not mushy, approximately 25 to 30 minutes. Recommended: serve with scoops of rum raisin ice cream.