Cook the beets: Wash, peel, and trim the beets. Place them in a pot of boiling water and cook for 30-40 minutes until tender. Reserve the cooking water. Let the beets cool before grating or blending.
Prepare the dairy base: In a large bowl, whisk together kefir, buttermilk, or yogurt with sour cream. Slowly add some of the cooled beet cooking water to adjust consistency.
Combine ingredients: Stir the grated or blended beets into the dairy base. Add lemon juice, minced garlic (if using), salt, and black pepper. Mix well.
Chill the soup: Cover and refrigerate for at least 2 hours or overnight for best flavor.
Prepare garnishes: Finely chop cucumber, radishes, dill, and green onions. Hard-boil, peel, and cut the eggs.
Serve: Ladle chilled soup into bowls. Top with cucumber, radishes, dill, green onions, and a boiled egg. Drizzle with sour cream if desired.
Enjoy: Serve cold with rye bread or fresh baguette.