Heat olive oil and butter in a large pot or Dutch oven over medium heat; cook and stir onion, garlic, carrot, and celery until softened, 5 to 10 minutes. Add parsley, basil, bay leaf, thyme, chicken broth, and tomatoes; bring to a boil. Reduce heat and simmer until heated through, 10 minutes.
Stir cabbage, kidney beans, and quinoa into the soup. Cover and simmer until quinoa is tender, 30 minutes. Garnish each serving with Parmesan cheese.