Place the cast-iron pan and lid together and heat them for 5 minutes on the stove top over medium heat. Lift the lid and add both halves of the brioche buns to the grill. Toast for 1 minute to bar-mark the insides.
Remove the buns and add lettuce leaves to each. Evenly distribute the cooked pork belly slices, chopped kimchi and pickled carrot. Prepare the eggs,