For Pork Chops Brine: To brine pork, combine salt, sugar and the 4 cups water in a large glass or enamel bowl, mixing until dissolved.
Add peppercorns, thyme and bay leaves and refrigerate until cold, about 30 minutes.
Place pork chops in a large resealable ziplock bag, cover with brine and close tightly. Place the bag in a large bowl and refrigerate for 24 hours.
To Finish Pork Chops: Preheat a barbecue grill to 400°F.
Line a plate with paper towels. Using tongs, remove pork chops from the brine and set on the lined plate to absorb any liquid. (If the pork chops are damp, the meat will flame on the barbecue.) Discard the brine. Allow pork chops to come to room temperature, 15-20 minutes, then season with salt and black pepper and brush lightly with olive oil.
Grill chops for 5 minutes, then turn them 45° and cook for another 5 minutes. Turn chops over, and grill for 5 minutes, then turn them 45° and grill for 5 minutes more. Insert a meat thermometer; once the meat reads 160°F, immediately remove chops from the heat and allow to rest for 5 minutes.
Fold pecans into the apple-pineapple relish. Divide the Brussels sprouts mixture between each of 4 plates. Place a pork chop over the sprouts and spoon a tablespoon of the apple mixture on top. Serve immediately.
To Make Apple-Pineapple Relish: In a large bowl, toss apple with lemon juice until well coated. Add pineapple, rice vinegar and honey and set aside. This relish will keep (without the pecans, which are added just before serving) refrigerated in an airtight container for up to 4 days.
For the Braised Brussels Sprouts: Line a small plate with a paper towel. In a medium frying pan on medium heat, cook bacon until lightly crispy, about 5 minutes. (If the meat begins to smoke, reduce the heat.) Remove bacon from the pan and drain on the lined plate. Carefully pour off some of the rendered fat, then add shallots and cook for another 2 minutes. Stir in Brussels sprouts and cook for 2 more minutes, then add bacon and butter and toss lightly. Season with salt, black pepper and lemon juice. Remove from heat and stir in Parmesan cheese.