Before you start cooking: Peel and finely chop 1 medium onion, then peel and dice 4 medium potatoes.
In a heavy-bottomed pot, heat 1 Tablespoon sunflower oil over medium heat. Add the onions and cook, stirring until translucent.
Add 2 teaspoons ground caraway seeds and stir for about 1 minute until the caraway aroma develops. Add 2 Tablespoons all-purpose flour and stir for 1 minute.
Remove the pot from the heat, then add one cup of lukewarm broth. Stir carefully with a whisk to prevent lumps. Add another cup of broth and whisk again. Now, add the rest of the broth, season with salt and ¼ teaspoon ground black pepper, and stir well.
Return the pot to the stove and add the diced potatoes. Increase the heat and bring the soup to a boil.
Reduce the heat to low, cover the pot with a lid, and let the soup simmer for 15 minutes, or until the potatoes are soft. Stir occasionally to prevent the flour from settling at the bottom and burning.
Finally, remove the pot from the stove, crack 1 egg into the soup, and whisk it in. Do not cook the soup any further.
Salt to taste if necessary, stir well, and serve, sprinkling each bowl of soup with chopped parsley greens.