In a large saucepan, combine the chicken thigh, whole onion, whole carrot and bay leaves. Add the water and bring to a simmer. Simmer 15-20 minutes, skimming any foam. Add the salt.
While the stock is cooking, saute the diced onion, grated carrot and garlic in the olive oil. Season with salt and pepper and remove from the heat.
When the chicken is cooked, remove the onion and carrot and discard. Remove the thigh and let cool slightly, then dice or shred. Return the chicken to the stock.
Add the potato to the soup and simmer 5 minutes. Add the sliced cabbage with the sauteed onion and carrot to the soup. Simmer another 5 minutes and adjust the seasoning. Serve hot, garnished with dill.