In a big soup pot, heat the oil over moderate heat. Add the onion and garlic and sauté for 7 minutes or until the onion is soft.
Add the carrots and sauté for 5 minutes or until the carrots are crisp-tender.
Stir in the cabbage, cover and cook, stirring occasionally for 10 minutes or until the cabbage is wilted.
Add the broth, 2 ½ cups water, dill, tomato paste, ginger, salt and pepper. Bing to a boil. Reduce heat and simmer for 15 minutes or until the cabbage is very tender. Stir the sour cream into the soup.