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put soy sauce, mirin, garlic and scallions in a medium saucepan over medium-low heat.
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cook until bubbling, 3 to 4 minutes.
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turn off heat and let cool slightly.
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prepare charcoal or gas grill; heat should be medium and rack about 4 inches from fire.
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sprinkle chicken with salt and pepper on both sides.
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remove scallions from soy mixture with slotted spoon and divide evenly among chicken cutlets:
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turn wide side of each cutlet to face you and put 2 or 3 scallions on edge closest to you, with some scallion sticking out of each end.
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roll each cutlet up like a jelly roll and secure in two or three places with toothpicks or butcher’s twine.
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brush chicken rolls with sesame oil.
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grill chicken, brushing occasionally with remaining soy mixture and turning each piece once or twice, until cooked through, 12 to 15 minutes.
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serve hot, warm or at room temperature with lemon or lime wedges.