Heat grill to medium (350° to 450°). Combine soy sauce, chili garlic sauce, oil, vinegar, sugar, and garlic in a small bowl. Set bok choy in a rimmed baking dish and brush with two-thirds of soy-garlic mixture. Wrap bok choy tops with foil.
Grill bok choy, turning once, until slightly softened and streaked brown, 5 to 6 minutes total. Remove foil from leaves and set bok choy on a platter. Brush with remaining soy-garlic mixture and sprinkle with cashews.