Combine the water, soy sauce, brown sugar, mirin and garlic to a 1 gallon freezer bag and shake to mix well. Add the chicken, then seal the bag, pressing out as much air as you can. Let the chicken marinate for at least 1 hour, or preferably overnight in the refrigerator.
While the chicken marinates, put the cucumbers in a bowl and sprinkle with the salt. Toss to coat evenly and let it stand for 30 minutes. When the cucumbers have started turning translucent, grab use your hands to squeeze out as much water as possible. The more water you squeeze out, the crunchier the pickles will be.
To make the sauce, add the miso, ground sesame seeds, yuzu juice, and water to a bowl and whisk to combine.
Remove the chicken from the marinade and discard the marinade. Get a charcoal grill going and grill the chicken, skin side down, until the skin is golden brown and crisp. If the chicken starts burning, move it over to the cooler side of the grill. Flip the chicken over and continue grilling until the chicken is cooked through (165 degrees F on an instant-read thermometer). Transfer the chicken to a cutting board and chop it into chunks.
To make the lettuce wraps, have each person grab a leaf of lettuce and add a spoonful of grilled chicken. Top with some pickled cucumbers and drizzle with a little sesame miso sauce. Wrap and enjoy!
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.