In a large pot over medium heat, heat the olive oil. Add the onion and garlic and cook until softened, about 5 minutes. Add the thyme and mushrooms and cook until the mushrooms are softened, about 7 minutes.
Add the farro, vegetable broth, and white wine (if using). Bring to a boil then reduce heat to low. Simmer for 25 minutes or until the farro is tender.