Slice each bok choy lengthwise, keep core intact on both halves. Trip ends and place in bowl.
Drizzle veggies with oil and sprinkle with salt and pepper. Place on a hot grill and char both sides until grill marks form, and veggies are tender (about 10 minutes).
For sauce mix together all ingredients then pour into a small skillet. Bring to a boil, stirring until sugar dissolves. Lower heat and simmer until reduced by half, about 15 minutes.
Strain sauce through a sieve (discarding solids), then drizzle over grilled veggies to serve.