Place the kielbasa and eggs (still in their shells, they are going to be hard-cooked) into a 4-quart pot and cover with the water and bring to a boil over high heat; reduce heat, cover, and simmer gently for 8 minutes.
Use a slotted spoon, to remove eggs to an ice water bath; continue simmering the kielbasa for 15 minutes more.
Drain kielbasa, reserving the cooking liquid separately.
Return the pot to the heat melt the butter; turn the heat up to medium and stir in the garlic and leeks and cook until softened, about 5 minutes.
Reduce heat and cook until leeks are very tender, about 20 minutes, being careful not to let the leeks brown.
Stir in the potatoes and reserved cooking liquid, increase heat to a simmer, cover, and continue cooking until potatoes are tender, 25 to 30 minutes.
Puree the soup using an immersion blender, or in a standing blender, in batches; return soup to medium-low heat.
In a small bowl, whisk together the flour and sour cream; stir in 1/2 cup of the soup to temper the mixture, then whisk into the soup in the pot on the stove.
Slice the kielbasa into 1/2-inch slices and stir into soup; stir in horseradish and season with salt and pepper.
Thin soup with water if needed.
Peel the eggs and roughly chop them as a garnish for the soup.