The night before grilling the chops, or even couple of hours before grilling, mix well in a medium bowl all the brine ingredients and half the water quantity and then add the chops to the brine mixture. Top up with water to cover the chops, cover with plastic wrap and refrigerate.
Next day, an hour before grilling take the chops outside the refrigerator, pat them dry with paper towel and season with salt and pepper both sides and edges. Keep aside.
For the Caramelized Onions:
Set a medium saucepan over high fire and let it heat up for 1-2 minutes. Add oil to the pan and swirl for a minute to heat up. Add the onions and sauté for a minute.
Reduce the heat to low, add the rosemary sprigs, sugar and the balsamic vinegar, sprinkle with the salt and pepper and cook slowly, stirring occasionally until well caramelized, 15 to 20 minutes. Keep aside warm.
For the Grilling:
Prepare your coals and once well rested and having created a nice grey ash, move them to the half of your grill.
Place your pork chops on the grill above the direct fire and sear each side for couple of minutes. Then move to the indirect heat area, cover and let cook for about 10 minutes flipping them once.
In the meantime, place on the grill over the direct fire the beet roots, lemons, tomatoes and broccoli, tossing every now and then and brushing with the olive oil. Just before they are ready sprinkle over them some salt and pepper.