Place all of the brine ingredients and 2 cups of water in a large pot and bring to a boil, stirring to dissolve the sugar and salt. Transfer to a large container and add 2 cups of cold water to dilute and cool the mixture. Chill until the brine is below 40°F. Add the pork chops and brine overnight.
To make the apple sauce, combine all of the ingredients in a medium-sized pot. Bring to a boil, reduce heat to a simmer, cover and cook for 15-20 minutes, until the apples are broken down and soft. Mash them with a whisk and cook for 10-15 more minutes , uncovered, until thickened. Adjust seasoning with more lemon or sugar if you like.
In a large skillet, melt half of the butter for the cabbage (2 tablespoons) over medium-low heat. Add the onions and sauté until softened but not colored, 5-7 minutes. Add the cabbage, vinegar, mustard seeds, caraway, sugar, salt and pepper and cook until the cabbage is softened. Stir in the remaining butter and season with salt and pepper.
In a small saucepan, combine all of the cider glaze ingredients and bring to a boil. Reduce the heat to low and simmer until reduced by ⅓.
Preheat the oven to 375°F. Heat a grill or large skillet to high heat.
Remove the pork chops form the brine, pat dry with paper towels, brush with oil and season with salt and pepper.
Sear the pork chops on each side for 2-3 minutes, until browned. Transfer to a baking sheet and brush with cider glaze. Finish cooking in the oven to reach desired doneness, 17-20 minutes. They should register at least 145°F internal temperature. Let the meat rest for 5 minutes before serving.
Meanwhile, return the remaining cider glaze to a simmer and reduce until syrupy. Brush the cooked pork chops with remaining glaze.
To serve, divide the mashed potatoes and applesauce between plates. Top with a pork chop and cabbage and sprinkle with chives.