Sauté the Aromatics: In a large Dutch oven or heavy-bottomed pot, heat the extra virgin olive oil over medium heat. Add the chopped leek, celery, and grated carrot. Sauté for 6-7 minutes, stirring occasionally, until the vegetables have softened and become fragrant. Add the minced garlic and cook for one minute more.
Cook the Chicken & Farro: Pour in the low-sodium chicken broth, then add the rinsed farro, the bay leaf, and a generous amount of black pepper. Submerge the whole chicken breasts into the broth. Bring the liquid to a gentle simmer, then reduce the heat to low, cover, and cook for 20-25 minutes, or until the chicken is cooked through and the farro is tender.
Shred the Chicken: Using tongs, carefully remove the cooked chicken breasts and transfer them to a cutting board. Allow the chicken to cool for a few minutes, then use two forks to shred the meat into bite-sized pieces. Set aside. Remove and discard the bay leaf from the pot.
Create the Lemon-Egg Emulsion: In a blender, combine the 3 large eggs, fresh lemon juice, and lemon zest. Ladle about 1 cup of the hot broth from the pot and add it to the blender.
Temper the Eggs: Seal the blender lid, remove the center cap, and cover the opening with a folded kitchen towel to allow steam to escape. Blend on low, gradually increasing to high, for about 30 seconds until the mixture is completely smooth, pale, and frothy.
Thicken the Soup: Ensure the soup in the pot is at a very low simmer, not boiling. Slowly pour the blended egg-lemon mixture back into the pot while whisking constantly. Continue to stir as the soup thickens for 2-3 minutes. It is crucial not to let the soup boil, as this will cause the eggs to curdle.
Combine and Serve: Stir the shredded chicken back into the thickened soup and allow it to heat through for another 2 minutes. Taste and adjust with more black pepper if needed. Ladle the soup into bowls and garnish generously with the fresh chopped herbs.