Heat the olive oil in a Dutch oven or heavy pot over medium heat. Add the onion and garlic; cook, stirring occasionally, until soft and glistening, about 6 minutes. Add the paprika and 1 teaspoon salt; cook until the oil turns deep red, about 1 minute. Add the flour and cook until just toasted, 30 more seconds. Immediately whisk in 4 cups water. Add the kielbasa, carrots, parsnips, potatoes and 1 1/2 teaspoons salt.
Bring the soup to a boil, then reduce to a simmer; cover and cook until the vegetables are tender and the broth has thickened, about 20 minutes. Add the vinegar and season with pepper.
Combine about half of the parsley with the sour cream in a small bowl and season with salt and pepper. Ladle the stew into bowls; top with the remaining parsley, a dollop of herbed sour cream and a sprinkle of paprika. Serve with bread.