Place sliced potatoes and beets in a medium saucepan over high heat; cover with stock, and boil until vegetables are tender. Remove potatoes and beets with a slotted spoon, and reserve stock.
Pour olive oil in a large skillet over medium heat. Stir in onions and salt; cook until onions become soft and translucent. Then stir in celery, carrots, and cabbage. Mix in reserved stock; cook, covered, until all vegetables are tender, about 10 minutes.
Add potatoes and beets to the skillet. Season with black pepper. Stir in cider vinegar and honey. Cover, reduce heat to medium-low and simmer at least 30 minutes. Serve topped with sour cream, dill weed, or chopped fresh tomatoes.