Dice the onions and tomatoes, mince the garlic, slice the carrot into coins, and thinly shred the cabbage. To a pot over medium heat, add the olive oil, onions, green onion, and carrots. Sauté for 5 minutes until soft and fragrant.
Add the garlic, oregano, red chili flakes, salt, and black pepper. Sauté for another minute until the garlic is fragrant. Add a 2 tbsp. of water to deglaze the pan and sauté for another 30 seconds.
Add in the diced tomatoes and tomato paste. Mix to combine to ensure that all ingredients are well coated in the aromatics. Cook for 5 minutes while constantly stirring.
Add the vegetable broth and bring the mixture to a boil. Add the shredded cabbage and stir. Simmer uncovered for 15 minutes until the cabbage softens and the liquid has slightly reduced.
Taste the soup, adjust the seasoning to your liking, and then add the heavy cream. Serve the soup in a bowl and garnish it with shredded cheese and a fresh crack of black pepper. Store leftover soup in an airtight container in the fridge for 3-5 days.