In a medium saucepan, place the beets and cover them with water by about 2 inches. Bring to a boil over medium-high heat and cook until the beets are easily pierced with a knife, 30 to 40 minutes. Drain the beets and let them sit for about 10 minutes. Peel then coarsely grate them when they are cool enough to handle. Return them to the pot. 

Coarsely grate 2 of the eggs and add them to the beets. Add the kefir, about ½ each of the cucumbers and radishes (reserve the remainder for finishing the soup), the dill and parsley. Mix everything together with a spoon. The mixture should be the consistency of a yogurt soup. If it is too thick, add a bit of the chilled water. Season to taste with salt and pepper. Cover the pot and chill for at least 30 minutes or up to 2 hours before serving. 

When ready to serve, halve the remaining 3 eggs lengthwise. Ladle the soup into bowls. Top each serving with some of the remaining cucumbers and radishes, green onions, egg halves, a dollop of yogurt, some dill and parsley, and a generous drizzle of oil. The soup needs to be eaten very cold, right from the fridge. It tastes best the day it is made.