Bring a large pot of salted water to a boil. Add the bok choy and parcook for about 3 minutes.
Meanwhile, in a bowl, whisk together all of the other ingredients.
Drain the bok choy and cut each head in half lengthwise. Add them to the sauce and toss to coat.
Preheat the grill to 500°F and oil the grates with high heat cooking oil.
Place the bok choy on the grill cut side down. Keep the bowl with the leftover sauce on the side. Flip the bok choy after about 5 minutes and brush with sauce.
Remove the bok choy when it is heated thoroughly and charred. Transfer to a plate for serving and drizzle the remaining sauce on top.