Make the ginger sauce by whisking together the soy sauce, vinegar, water, sesame oil, scallion, and 1 tablespoon of the ginger. Set aside. Heat broiler to high. Brush both sides of the pork chops with the olive oil, then sprinkle with the salt and the remaining ginger. Broil 2 minutes on each side. Cool and slice thinly. Arrange the lettuce leaves on a platter and fill each with some cilantro, carrots, cucumbers, and sliced pork. To eat, drizzle with the ginger sauce and roll the lettuce leaves to close. Serve with plenty of napkins.
To Make Ahead: Make and refrigerate the dipping sauce up to 3 days beforehand. Prepare the remaining ingredients and wrap separately in resealable plastic bags a day in advance.