Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Add mushrooms and cook until golden and liquid evaporates, about 8 minutes.
Season with salt and pepper, set aside.
Heat remaining oil in a large saucepan over medium heat.
Add onion and cook until softened, about 5 minutes.
Add garlic and barley, stirring for 1 minute.
Add wine if using, stirring until absorbed.
Add warm broth one ladle at a time, stirring frequently until absorbed.
Continue for 35-40 minutes until barley is creamy and tender.
Stir in cooked mushrooms, thyme, and nutritional yeast.
Garnish with parsley before serving.