Step 1Into a 4-quart heavy-bottom pot, place the kielbasa and the eggs (still in their shells). Add the water and bring to a boil over high heat. Reduce the heat, cover the pot and simmer gently for 8 minutes. Using a slotted spoon, transfer the hard-boiled eggs to a bowl of ice water to chill. Continue to simmer the kielbasa for another 15 minutes, then remove from heat. Drain the kielbasa, saving the cooking water and kielbasa separately.
Step 2Return the pot to the stove and melt the butter over medium heat. Stir in the garlic and leeks and cook until the leeks are softened, about 5 minutes. Reduce the heat and continue to cook until the leeks are very tender, about 20 minutes, being careful that the leeks do not brown or char as this will muddy the pale color of the soup. Stir in the potatoes and cooking water, then increase the heat to a gentle simmer. Cover and continue to gently simmer until the potatoes are tender, 25 to 30 minutes.
Step 3Using an immersion blender, or in batches using a stand blender, puree the leek and potato mixture until nearly smooth. Heat the soup over medium-low heat.
Step 4In a large cup or small bowl, whisk together the flour and sour cream to form a slurry. Stir one-half cup of the soup into the slurry to temper it, then whisk the slurry into the soup until thoroughly incorporated.
Step 5Slice the cooked kielbasa into one-half inch slices, and stir them into the soup. Stir in the horseradish, and season to taste with salt and pepper. The soup should have the consistency of heavy cream; adjust the consistency as desired with additional water.
Step 6Peel and roughly chop the hardboiled egg. Ladle and serve the soup in bowls, garnished generously with hardboiled eggs.