Soak the barley in warm water for 3 hours, then drain and set aside.
Preheat an oven to 350 degrees F.
Heat a large skillet over medium-high heat and stir in the beef and onion. Cook and stir until the beef is evenly browned, about 10 minutes. Drain and discard any excess grease, then stir in the mixed vegetables, soy sauce, molasses, drained barley, and 1 1/2 cups of water. Stir until the molasses has dissolved and the mixture has begun to simmer. Season to taste with garlic powder, salt and pepper, then pour into a lidded 2 quart casserole. Add bay leaf.
Bake, covered, in the preheated oven until the barley is tender and has absorbed the water, about 1 hour.