The healing quality of this tangy, fortifying soup comes, ostensibly, from a fermented sour rye soup starter called zakwas. Though you can buy it at Polish markets, it takes just a few minutes to mix it up yourself. Just build in a few days to your soup-making plan for the fermentation to take place. The hearty combination of root vegetables, kielbasa, pickles, sour cream, and hard-boiled eggs makes this soup a meal.
For the zakwas: Pour 2 cups boiling water into a heatproof 1-quart jar or glass bowl. Let cool to warm.
Stir the flour, garlic, and bay leaf into the warm water. Tightly cover/seal the jar or bowl with plastic wrap (use a rubber band or two to hold the wrap tightly) and let sit in a warm, dark place (like a cupboard) for 4 to 5 days; “burp” the mixture every 2 days by removing the plastic wrap to let the air out, then resealing it again (this will prevent a little culinary explosion). Alternatively, you can seal the jar or bowl with cheesecloth (more breathable), held tightly with a rubber band, and you will not have to burp the mixture.
The zakwas is ready when it has a pungent fragrance, a solid, spongy deposit on top, and a light brown-gray liquid at the bottom. Scrape off any green or moldy bits that appear on the top (a healthy sign of the fermentation process and not dangerous!), and remove and discard the bay leaf. Strain the zakwas through a sieve into a bowl; discard the solids. You’ll have about 1½ cups liquid. Use however much you have; the exact amount is not important.
For the soup: In a large Dutch oven or other wide heavy pot, cook the bacon over medium-high heat, stirring occasionally, until golden and crisp, 5 to 7 minutes. Using a slotted spoon, transfer to a medium bowl. Add the onions to the pot and cook, stirring occasionally, until tender and lightly golden, 12 to 14 minutes. Transfer to the bowl with the bacon. Add the kielbasa or bratwurst to the pot and cook, stirring occasionally, until golden brown, 12 to 15 minutes. Transfer to the onion mixture. Pour off and discard the fat from the pot.
Add the carrot, parsnip, celery root, parsley sprigs, bay leaves, marjoram, allspice, 1 teaspoon salt, and 7 cups water to the pot, bring to a simmer, and cook until the vegetables are almost tender but with a little bite, 12 to 15 minutes.
Add the zakwas, horseradish, and onion mixture to the pot, return the soup to a simmer, and cook until the vegetables are tender and the broth is flavorful, 10 to 12 minutes. Stir in the white pepper. Season to taste with salt. Remove and discard the parsley sprigs and bay leaves.
Spoon the soup into bowls. Top each bowl with a big dollop of sour cream, a hard-boiled egg half, the chopped pickles, and some dill or parsley, and serve.