Cook and stir bacon in a large pot until browned, about 5 minutes. Add onion and garlic; cook until soft, about 5 minutes.
Pick meat off the duck bones and chop. Discard skin and bones. Add duck meat to the pot. Stir in chicken stock, navy beans, cabbage, turnips, celery, thyme, rosemary, and sage. Tie parsley and bay leaf together; add to the pot. Simmer until turnips are tender, about 1 hour.
Stir potatoes and carrots into the pot; cook until soft, about 20 minutes. Discard parsley sprigs and bay leaf. Season soup with salt and pepper.