Brown the ground beef in a large pot or Dutch oven. Drain off any excess grease.

Add the chopped onion and minced garlic to the pot and cook until softened, about 5 minutes.

Stir in the crushed tomatoes, beef broth, rice, and tomato paste.

Add the shredded cabbage, dill, salt, and pepper. Bring to a boil, then reduce heat and simmer for 45-60 minutes, or until the cabbage and rice are tender.

Serve hot.