Peel and wash the vegetables. Also, wash the chicken parts and dry them with a paper towel. Put the chicken parts and the vegetables in a large pot, add bay leaves and half of parsley and dill. Fill the pot with water and bring it to boil. Don't cover.
When the soup boils, you'll see fat and foam on top of it. Carefully skim the fat and the foam carefully from top, while trying not to mix the soup. The more foam you skim, the clearer the soup will be. After you finished skimming, lower the heat and cook it the soup for another 30-40 minutes, while checking that there is no more foam on top. Season with salt and pepper.
When done, you can strain the soup through a fine colander into another pot or a bowl, or you can just take out all the cooked vegetables and chicken parts. Throw out the cooked onion, celery and herbs. Grate the carrot and put it back in the soup. Chop the other halves of fresh parsley and dill and add it to the soup. Separate the chicken meat from the bones, chop it and add it to the soup. Check the seasoning before serving,