Chop the cooked beef into bite-size pieces and set aside.
In a large soup pot, heat oil over medium heat and sauté onions and celery until softened. Remove and set aside.
In the same pot, add water, beef bouillon cubes, sugar, 1/4 teaspoon pepper, stewed tomatoes, bay leaf, chopped beef, and barley.
Bring the mixture to a boil, then reduce heat and simmer for 10-15 minutes.
Add the sautéed vegetables and frozen mixed vegetables to the pot.
Cook until thoroughly heated and vegetables are tender.
Remove bay leaf and season with salt and pepper to taste before serving.