Rinse the farro under cold water. Place it in a medium pot with 3 cups of water and a pinch of salt. Bring to a boil, then reduce heat and simmer for 25 to 30 minutes until tender but still chewy. Drain any excess water and let the farro cool slightly.
In a small bowl, whisk together the olive oil, lemon juice, oregano, salt, and pepper to make the dressing.
Flake the drained tuna into a large mixing bowl. Add the cooked farro, cherry tomatoes, cucumber, olives, and red onion.
Pour the dressing over the mixture and toss gently to coat everything evenly.
Add the mixed greens and feta cheese. Toss once more just before serving so the greens stay crisp.