Tie the stems of the cilantro and dill into bundles, then trim off the leaves, reserving ¼ cup of each for garnish. In a large pot, combine both sets of stems, the chicken and the remaining ingredients. Bring to a boil, then reduce heat to medium-low and simmer for 45 minutes. Remove the garlic head and transfer the chicken to a plate and cool until easily handled. Once cool, shred the chicken into bite-size pieces, discarding the skin, bones and cartilage. Set aside.