Rinse the farro thoroughly under cold water in a mesh strainer and set aside.
Heat the oil in a dutch oven over medium-high heat. Add the onion, carrot, and celery and cook, stirring occasionally, until vegetables are softened, about 5 minutes.
Add the mushrooms, 1 tsp salt, and ½ tsp pepper to the pot and cook, stirring occasionally, until mushrooms are browned, about 7 minutes.
Stir in the garlic and cook until fragrant, about 15 seconds.
Add the vegetable broth, bay leaves, sage and farro to the pot and bring to a boil. Reduce heat to medium-low and simmer, stirring occasionally, until farro is cooked, about 30 minutes.
Remove the bay leaves and season the soup with salt and pepper to taste.
