Begin by peeling and grating fresh beets. Please take note of using gloves to avoid staining your hands. Next, place the grated beets in a large pot or Dutch oven, and cook them in vegetable broth or water until they become tender, which typically takes about 10 minutes. Allow the cooked beets to cool completely. To expedite this cooling process, you can set the pot with the beets in a sink filled with a few inches of icy cold water.
Grate the cucumber; there's no need to peel it. Grate or finely chop the radishes. Prepare the herbs by chopping them and setting them aside.
In the pot containing the cooled beets along with their liquid, incorporate kefir, yogurt, the prepared cucumber, radishes, and herbs. Mix everything thoroughly. Season the soup with salt and pepper and introduce lemon juice and apple cider vinegar if desired.
Cover the pot and place the soup in the refrigerator to chill for a minimum of 3 hours. When serving, ladle the soup into bowls and top each serving with a quartered hard-boiled egg, either warm or cold.