Preheat oven to 375 degrees. In a bowl, combine brown sugar, butter, cinnamon, nutmeg, flour and salt. Whisk to combine. Slice each half of an apple into thin slices three quarters of the way down, leaving the bottom of the halved apple intact. (This method of slicing is called Hasselback.) Place apple halves flat side down in a baking dish. Spoon or brush half of the brown sugar/butter mixture over the apples. Cover and bake for 25 minutes or until apples are cooked but still slightly firm. Meanwhile, make chicken.
For the Chicken:
Combine the apple cider vinegar, soy sauce, maple syrup, honey or agave nectar and ground pepper in a bowl. Whisk to combine and then set aside. Wash and pat the chicken thighs dry. Sprinkle liberally with salt and pepper on both sides. In a cast iron or heavy skillet, heat oil. When hot, add chicken thighs and cook until browned on both sides. When the second side is browned, spoon the glaze over the thighs. Reduce heat to medium high and cook until chicken is done and sauce is slightly thickened. Spoon remainder of the apple glaze over the baked apples and return to oven, uncovered for 5 minutes. Serve 2 pieces of chicken thighs and one apple half per serving.