Brown the ground beef in a skillet over medium heat, breaking it up as it cooks. Add the onion and garlic and cook until the onion softens.
Transfer the beef mixture to the slow cooker. Add the carrots, potatoes, cabbage, diced tomatoes, beef broth, salt, and pepper.
Stir everything together, cover, and cook on low for 7 to 8 hours until the vegetables are tender.
Stir in the fresh dill right before serving.