In large pot of boiling water, cook cabbage just until outer leaves pull away easily from head, removing and draining leaves until all are blanched, about 3 minutes. Cut out thick vein from bottom of each leaf.
Meanwhile, in large bowl, combine barley, onion, garlic, soy sauce, ketchup, brown sugar, ginger, salt and pepper. Add beef and mix well.
Place about ½ cup (125 mL) beef mixture on each of 14 cabbage leaves; fold in sides. Beginning from cut end, roll up; repeat with remaining leaves and meat mixture.
Place rolls, seam side down, snugly in greased 13- x 9-inch (3.5 L) baking dish.
In bowl, combine sauce ingredients. Pour over rolls. Cover tightly with foil and bake, with rimmed tray underneath, in preheated 350°F (180°C) oven until an instant-read thermometer placed in centre of a roll reads 160°F (70°C), 80 to 90 minutes.