Heat the olive oil in a large pot over medium-high heat. Add the onion and shredded carrot and cook for 3–4 minutes, stirring occasionally.
Add the garlic and cook for 30 seconds, until fragrant.
Add the thinly shredded cabbage, lentils, diced tomatoes, tomato sauce, vegetable broth, brown sugar, vinegar, tamari, smoked paprika, Italian seasoning, garlic powder, onion powder, salt and pepper. Stir well.
Increase the heat and bring to a boil. Reduce to a lively simmer, partially cover, and cook for 10–12 minutes, stirring occasionally, until the cabbage is tender.
Stir in the cooked rice or quinoa and parsley. Cook for another 2–3 minutes, just until heated through. Taste and adjust salt, pepper, vinegar or broth as desired.
Serve hot with parsley, dill, chives, green onion, vegan sour cream, or a light sprinkle of smoked paprika.