In a medium saucepan combine the brine ingredients. Bring to a boil over high heat and simmer for 2 minutes. Remove the pan from the heat and let the brine cool completely.
Place the pork chops in a large, resealable plastic bag and pour in the cooled brine. Press the air out of the bag and seal tightly. Turn the bag to distribute the brine, place the bag in a bowl, and refrigerate for 6 to 24 hours, turning occasionally.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
In a small saucepan combine all of the sauerkraut ingredients except the apples. Bring the mixture to a simmer over medium heat, cover the saucepan, and simmer for about 10 minutes, stirring occasionally. Stir in the apple, remove from the heat, cover, and set aside until ready to serve.
Remove the chops from the bag and discard the marinade. Pat the chops dry with paper towels. Lightly brush the chops on both sides with oil and season evenly with the salt and pepper.
Brush the cooking grates clean. Grill the chops over direct medium heat, with the lid closed, until they are still slightly pink in the center, 8 to 10 minutes, turning once or twice. Serve warm with the sauerkraut and the whole-grain mustard on the side.