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For the sauce:
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In a small, heavy saucepan combine the sauce ingredients and bring to a simmer over medium heat. Let the mixture simmer for 6 minutes. Add the scallions and let them cook for another 6 minutes until they are soft but not mushy.
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Remove the pan from the heat and set aside to cool.
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For the chicken:
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Lay out the chicken breasts on a sheet of waxed or parchment paper with the pointed end facing you and the wider end facing away.
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When the scallions have cooled, place 2 of them on the shortest side of the breast, about 1 inch from the edge. Reserve the sauce.
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Tuck the bottom edge over the scallions and make a tight roll. Tie them with two pieces of cotton twine.
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Do the same for the other breasts.
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Brush the breasts with the oil and set aside until you are ready to grill them.
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Preheat the grill or a grill pan to medium high heat (about 400 degrees). Place the chicken bundles on the grill and grill for 8 minutes per side.
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Reheat the sauce over very medium heat until it thickens, about 5 minutes. Keep a close eye since it burns easily.
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Remove the chicken breasts from the grill and serve the breasts whole or sliced over a bed of basmati rice or Chinese noodles which you have tossed in some sesame oil.
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Garnish with toasted sesame seeds.