Cook and stir beef in a large saucepan or Dutch oven until browned, about 5 minutes; drain excess grease.
Stir beef bouillon into chicken broth in a bowl until dissolved; add to beef.
Mix onions, Greek seasoning, black pepper, and bay leaves into broth-beef mixture; cover saucepan and simmer until beef is tender, about 1 hour 15 minutes. Add cabbage and celery to broth-beef mixture; cover saucepan and simmer until celery is tender, about 30 minutes more.
Stir plum tomatoes, tomato sauce, and salt into broth-beef mixture and simmer, uncovered, until stew is slightly thickened, 15 to 20 minutes. Remove and discard bay leaves before serving.
Cook's Note: Beef broth can be substituted for the chicken broth.