The red theme—beets, onions, cabbage, tomato paste, vinegar—may be playful, but that combination also adds enormous depth to this vegetarian spin on classic borscht. Slideshow: Vegetarian Soup Recipes
Heat the olive oil in a large pot over moderate heat. Add the carrots and onions and cook, stirring occasionally, until softened, about 10 minutes. Push the vegetables to one side of the pot and add the tomato paste. Cook, stirring constantly, until the paste is fragrant and turns a shade or two darker, about 1 minute. Add the caraway seeds and stir everything together.
Add the beets, cabbage and water. Bring to a boil, then reduce heat to moderately low and simmer until vegetables are tender, about 45 minutes. Season to taste with the vinegar, salt and pepper.
Ladle the soup into warm bowls. Garnish with the chopped dill and serve immediately.
The soup can be made up to 5 days ahead.