In a large pot or Dutch oven over medium-high heat, brown the ground beef, breaking it into small pieces with a wooden spoon, about 5-6 minutes until no longer pink. Drain any excess fat.
Add the diced onion to the pot with the beef and cook for 3-4 minutes until softened, then add the minced garlic and cook for 1 minute more until fragrant.
Stir in the tomato paste, oregano, paprika, pepper, and salt, cooking for 1 minute to develop the flavors.
Pour in the beef broth and add the diced tomatoes, chopped cabbage, sliced carrots, and bay leaves. Bring the soup to a boil.
Reduce heat to medium-low and simmer uncovered for 20-25 minutes, stirring occasionally, until the cabbage is tender and the flavors have melded together.
Remove the bay leaves, taste and adjust seasoning if needed, then ladle into bowls and serve hot.