Whisk together the rice wine vinegar and 1 tablespoon of the sugar in a mixing bowl until the sugar dissolves. Add the grated carrot and stir to combine. Season with salt and reserve.
Combine the remaining sugar and 1/4 cup water in a small saucepan. Bring to a simmer over medium heat and simmer until the sugar dissolves, about 3 minutes. Turn off the heat and add the fish sauce, garlic, lime zest and juice and a pinch or 2 of red pepper flakes. Spoon out a 1/4 cup of the sauce to baste the pork chops and reserve the rest to serve with the rice bowls.
Heat an outdoor grill or large cast-iron grill over medium-high heat. Whisk together the 1/4 cup sauce and the oil and brush liberally all over the pork chops. Place the pork chops on the grill and cook until the pork is warmed through and charred on both sides, about 5 minutes total. The pork chops might stick a bit to the grill but that is okay - just use a pair of tongs to gently pull away as needed. Transfer to a cutting board and allow to rest for 5 minutes. Cut each pork chop off the bone and thinly slice against the grain.
To serve, divide the rice among 4 large bowls. Toss the carrots with the cilantro. Top each bowl with a few slices of the pork, divide the carrot salad among the bowls and top with the rest of the sauce. Stir to combine and serve.