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1
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.
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2
Use a slotted spoon, to remove eggs to an ice water bath; continue simmering the kielbasa for 15 minutes more.
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3
Drain kielbasa, reserving the cooking liquid separately.
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4
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.
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5
Reduce heat and cook until leeks are very tender, about 20 minutes, being careful not to let the leeks brown.
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6
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.
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7
Puree the soup using an immersion blender, or in a standing blender, in batches; return soup to medium-low heat.
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8
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.
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9
Slice the kielbasa into 1/2-inch slices and stir into soup; stir in horseradish and season with salt and pepper.
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10
Thin soup with water if needed.
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11
Peel the eggs and roughly chop them as a garnish for the soup.