Put chicken pieces in a large stockpot; pour enough water over chicken to cover completely.
Add onion, celery, bouillon cubes, basil, parsley, garlic, salt, and pepper to the pot; bring to a simmer over medium-high heat. Cook at a simmer until the chicken is cooked through and tender, about 1 hour.
Remove and discard celery chunks.
Remove chicken to a cutting board to cool; cut as much meat as possible from the bones and chop roughly. Return chicken to stock.
Stir potatoes, kohlrabi, carrots, and turnip into the soup; cook until the vegetables are tender, about 20 minutes.
Add cabbage, corn, green beans, and tomato; cook until the green beans are tender, 7 to 10 minutes more.