Heat olive oil in a 4qt Dutch oven over medium high heat.
Add the ground beef and let it cook for 3 to 4 minutes without stirring to form a nice crust on one side.
Break it up with a spoon, continue cooking until no pink remains. Drain any fat.
Add the onion and garlic and cook 3 minutes more.
Add the broth, scraping up any browned bits on the bottom of the pan.
Add the cabbage, diced tomatoes, tomato sauce, Worcestershire sauce, dill, salt and pepper.
Stir, cover, and simmer for 18 to 25 minutes or until the cabbage is tender, stirring occasionally.
Simmer uncovered for 3 to 5 minutes to thicken if desired.
Season with additional salt and pepper to taste.
Serve over rice or pasta if desired.
