In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until browned. Drain off any excess grease.
Add the chopped onion to the pot and cook until softened, about 5-7 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the shredded cabbage, beef broth, and diced tomatoes to the pot. Stir in the dried thyme, salt, and black pepper.
Bring the soup to a boil, then reduce the heat to low, cover, and simmer for at least 30-40 minutes, or until the cabbage is tender and the flavors have melded together. Stir occasionally.
Taste and adjust seasoning with salt and pepper if needed. Serve hot.
Notes
This cabbage soup is even better the next day as the flavors continue to develop. You can add other vegetables like carrots, celery, or potatoes for an even heartier soup.