Thoroughly rinse the white and green parts of the leeks. Bundle the green parts together and tie them together with kitchen twine. Set aside. Halve the white parts of the leeks lengthwise and thinly slice.

Place the chicken in a large pot and cover with 8–10 cups water. Add the bundled green parts of the leeks and the garlic. Season liberally with salt. Bring to a boil, reduce heat, and simmer, uncovered, for 1 hour. Skim off any foam or scum that floats to the top of the broth.

Remove and discard the bundled leeks. Transfer the chicken to a large bowl. Transfer the head of garlic to a small bowl.

Return the broth to a low boil and cook for 20 minutes to reduce the liquid to about 6 cups. Taste the broth and add more salt if you like. Strain the broth through a fine-mesh sieve into a large bowl and wipe out the pot.

Once the chicken is cool enough to handle, pick the meat from the bones and shred it with your hands or dice it into small pieces, depending on your preference. Carefully pop the garlic from the paper and mash it into a paste with a fork.

Heat 1 tablespoon extra virgin olive oil in the pot. Add the shallots, carrots, celery, white parts of the leeks, and potatoes. Cook for 8–10 minutes. Season with salt and pepper.

Add the garlic paste and chicken. Cook for 1 minute.

Pour in the chicken broth and bring to a boil. Once boiling, add the farro, reduce heat to low, and simmer for 30 minutes until the farro is tender and the potatoes are fork-tender. Taste and add salt and pepper if needed.

Stir in the dill and lemon juice and simmer for 5 minutes. Turn off the heat.

Ladle the soup into bowls and garnish with more dill. Serve with lemon wedges if you like. Enjoy!