Put chicken and onions in a large pot; pour in enough water to cover. Add dill, parsley, salt, and pepper. Bring to a boil, then reduce the heat to medium-low and simmer for 45 minutes.

Skim and discard any foam from the top of the simmering liquid. Remove chicken to a cutting board. Remove as much meat from the bones as possible and cut into chunks.

Return the broth to a boil. Add carrots, potatoes, leeks, celery, kohlrabi, and parsnips. Reduce the heat to medium-low and cook until vegetables are tender, about 20 minutes. Stir in cooked chicken and bouillon. Season again with salt and pepper. Cook until chicken is hot, about 5 minutes.