For the Brine: In a pot, combine all ingredients and 6 liters water. Bring to a boil. Remove from heat and add ice. Cool to room temperature. Reserve.
For the Pork Chops: In a nonreactive container, cover pork chops in Brine. Cover and refrigerate 24 hours.
For the Peperonata: In a pan over medium flame, heat oil. Add onion, garlic, and salt and cook until soft and translucent. Add peppers and oregano and cook until tender. Stir in vinegar and sugar.
For the White Bean Purée: In a medium-sized rondeau, heat pure olive oil. Add garlic and cook until toasted. Add beans. Cook until super creamy and emulsified. In batches, transfer to a food processor, add the remaining ingredients, and purée until smooth. Transfer to a nonreactive container and reserve.
For the Chicken Jus: In a large rondeau over high heat, caramelize chicken bones until well browned. Add pork bones, carrots, shallot, and celery and roast until browned. Deglaze with Marsala and vinegar. Add all remaining ingredients. Bring to a simmer. Continue to simmer until the jus is thick enough to coat the back of a spoon.
To Assemble and Serve: Prepare and heat a grill. Remove 1 Pork Chop from Brine and pat dry. Over medium flame, add the Pork Chop and grill until the internal temperature reaches 140°F. Remove from heat and let rest 8 minutes. Cut into ½-inch slices. In 3 separate, small pots, heat ½ cup White Bean Purée, ½ cup Peperonata, and 2 ounces Chicken Jus until warm. Spoon the White Bean Purée onto the center of a serving plate. Shingle the grilled pork chop above the White Bean Purée. Garnish with olives and the warm Peperonata. Pour the warm Chicken Jus over the pork. Finish with a sprinkle of sea salt.
