In a large Dutch oven over medium heat, warm the oil. Add leek, celery, and carrot; sauté 6–7 minutes until softened. Stir in garlic; cook 1 minute.
Add broth, farro, bay leaf, and black pepper; bring to a gentle simmer. Nestle in chicken breasts.
Simmer gently 12–15 minutes, then check chicken with an instant-read thermometer; remove when it reaches 165°F (74°C). Continue simmering the soup 25–30 minutes total, or until farro is tender. Discard bay leaf. Shred chicken.
In a blender, combine eggs, lemon juice, and zest. Carefully add about 1 cup hot broth; blend 30 seconds until smooth and frothy (lid vented).
Reduce soup to just-steaming (no bubbles). Slowly whisk in the egg-lemon mixture. Stir 2–3 minutes, keeping soup at 160–170°F (71–77°C); do not boil.
Return shredded chicken to the pot; warm 2 minutes. Season to taste with optional salt and more pepper.
Ladle into bowls and garnish with fresh herbs.