In a large pot over medium heat, brown onion, garlic, and beef until no pink remains. Drain any fat.
Add cabbage to pot and stir until slightly softened, 3-4 minutes.
Add remaining ingredients and simmer, covered, on low until cabbage is tender and soup is slightly thickened (about 30 minutes). Taste and season with additional salt and pepper if desired.
Remove bay leaf and serve.
Notes
For a smoother soup, try grating the cabbage in a food processor. Cabbage will cook faster and soak up more broth.
Sautee the cabbage in bacon grease for a smoky and delicious flavor addition.