In a medium bowl whisk the marinade ingredients, making sure to dissolve the sugar completely.
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Put the steaks in a large, resealable plastic bag and pour in the marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade, place in a bowl, and refrigerate for 8 to 12 hours, turning occasionally.
Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over medium heat (180° to 230°C).
Prepare the grill for cooking over medium heat (200°C).
Remove the steaks from the bag and discard the marinade. Brush the cooking grates clean. Grill the steaks over direct medium heat, with the lid closed, until no longer pink in the center, 8 to 10 minutes, turning once or twice. Remove from the grill and let rest for 3 to 5 minutes. Cut the steaks into bite-sized pieces.
Remove the steaks from the bag and discard the marinade. Brush the cooking grates clean. Grill the steaks over medium heat, with the lid closed, until no longer pink in the center, 8 to 10 minutes, turning once or twice. Remove from the grill and let rest for 3 to 5 minutes. Cut the steaks into bite-sized pieces.
Pick a whole lettuce leaf, spread a little gochujang (red chili paste) on top, if desired, arrange some steak and kimchi in the middle, and roll it up.
