In a large pot or Dutch oven, heat a drizzle of olive oil over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent, about 5 minutes.
Add the ground beef, breaking it up with a wooden spoon. Cook until browned and no longer pink, about 7-10 minutes. Drain any excess fat if necessary.
Stir in the tomato sauce, diced tomatoes, chicken broth, Worcestershire sauce, dried basil, and dried oregano. Bring the mixture to a simmer.
Once simmering, add the chopped cabbage and cooked rice to the pot. Reduce the heat to low, cover the pot, and let it simmer for an additional 25-30 minutes, stirring occasionally, until the cabbage is tender.
Taste the soup and adjust with salt and pepper as desired.
Serve hot, garnished with fresh herbs if desired.