Cook farro according to package directions.
Heat oil in heavy-bottomed deep pot. Sauté onions and carrots over medium heat or until onions begin to lose color, about 10 to 15 minutes. Add garlic and sauté for 30 seconds.
Add fresh mushrooms and cook until they begin to release liquid, about 5-10 minutes.
Raise heat and add broth and sherry vinegar. Season with salt and pepper and simmer for 30 minutes. Stir in cooked farro and cooking wine. Adjust seasonings and serve