To make this recipe on the stovetop, cut the beef into bite-sized pieces. Heat 1 tablespoon of vegetable oil in a stock pot over medium-high heat. Add the beef cubes and cook until browned on all sides, stirring frequently. Remove the meat and set aside. Reduce the heat to medium, add the remaining tablespoon of vegetable oil, and stir in the carrots, celery, and onion. Cook until the onion is translucent and the vegetables are tender, about 5 minutes. Add the water, bouillon, bay leaf, tomatoes, barley, sugar, and pepper; bring to a simmer. Stir in the beef cubes and simmer, covered, until the beef is tender and the barley is fully cooked, about 2 hours. Add the frozen vegetables in the last half hour of the cooking time.