Heat oil in a large Dutch oven or soup pot over medium-high heat until shimmering. Add the onion and cook until it starts to caramelize, about 5 minutes. Add the garlic and sauté for 30-seconds.
Add the ground beef, salt, pepper and crushed red pepper flakes (if using) to the Dutch oven. Sauté until the ground beef is cooked through. Drain the mixture and return to the pot.
Add the carrots, tomato sauce, diced tomatoes, soy sauce, brown sugar, vinegar and broth to the beef mixture. Add the cabbage and rice and bring to a boil. Reduce the heat to medium-low and cover with a tight fitting lid.
Simmer the soup, covered, for 20-30 minutes or until the cabbage is just tender and the rice is cooked.