Separate beet from tops, peel the beet, cut into stripes. Slice the beet top stalks, combine with beet and coat with hot water. Bring to simmering boil, add vinegar and sautee, covered, until almost ready.
At the end of the cooking add beet top leaves, cut in stripes, and boil for 5-7 minutes. Cool. Peel the carrots, cut in stripes and sautee until ready. Cool.
Peel the cucumbers, cut in stripes. Peel the onions, rinse and chop fine.
Mix part of sour cream, salt, sugar and onion, add carrots, beet together with water and beet tops, cucumbers, pour in kvass and stir thoroughly.
When serving up, pour soup into plates and put an egg-half into each, some sour cream and sprinkle with minced dill. Serve chilled to 50-60oF (14-16°С).