Heat oil in a large, heavy pot over medium heat. Season chicken with salt and pepper. Brown chicken in batches, skin-side down, until crispy. Remove chicken and set aside.
Add onion and carrots to the pot and cook until softened, about 5-7 minutes.
Add tomatoes and garlic and cook for another 2-3 minutes.
Return chicken to the pot. Add dill, bay leaves, wine, and water. Bring to a simmer.
Cover and cook for 1 to 1.5 hours, or until chicken is cooked through.
Remove chicken and set aside to cool. Add cabbage and potatoes to the pot and continue simmering for another hour, or until tender.
Remove chicken skin and bones, shred the meat, and return it to the pot. Skim any excess fat from the broth.
Taste and adjust seasoning as needed. Serve hot with crusty bread.