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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 degrees).
To make the sauerkraut mixture: In a small saucepan combine sauerkraut, 2 tablespoons brown sugar, butter, caraway seed and 1/4 teaspoon black pepper. Bring the mixture to a simmer over medium heat, cover the saucepan and simmer 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 1/2 teaspoon salt and 1/4 teaspoon 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.