Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Cook mushrooms until golden, about 6 minutes. Set aside.
Heat remaining oil in a large saucepan over medium heat.
Add onion and cook until softened, about 5 minutes.
Add garlic and farro, stirring for 1 minute.
Add wine if using, stirring until absorbed.
Add warm broth one ladle at a time, stirring frequently.
Continue for 35-40 minutes until farro is creamy and tender.
Stir in mushrooms, peas, and Parmesan.
Garnish with parsley before serving.