Heat the olive oil in a large pot over medium heat. Add the sliced leeks and cook for 4 minutes until they soften.
Stir in the minced garlic, diced carrots, and diced celery. Cook for another 3 minutes.
Add the rinsed farro and stir to coat it with the vegetables and oil.
Pour in the diced tomatoes and vegetable broth. Add the rosemary sprigs and bay leaves.
Bring the mixture to a simmer. Cover the pot and cook for 25 minutes, stirring once or twice.
Stir in the drained borlotti beans. Continue simmering uncovered for 10 minutes until the farro is tender.
Remove the rosemary sprigs and bay leaves. Season with salt and black pepper. Stir in the chopped parsley just before serving.