Heat oil in a large soup pot. Add onions, cook for 6-8 minutes until soft.
Add carrots, potatoes, and rutabaga and cook for 5-6 minutes, stirring.
Add the water or broth, and tomato paste, and bring to a boil.
Reduce heat to a simmer and cook for about 10-15 minutes. Add cabbage and cook for another 10-15 minutes, until all veggies are tender and cabbage is wilted.
Spoon out some of the hot broth and mix the miso and honey into it, then add back to the pot and stir.