Dry sauté the mushrooms by adding them to a large sauté pan and cooking them over medium-high heat. Cook the mushrooms for about 4 to 5 minutes, until they start releasing their liquids, stirring frequently. Transfer the mushrooms and juices to a bowl. Wipe down the pan.
Heat 2 tablespoons of olive oil in the pan over medium-high heat. When the oil is hot, add the onion and salt, and cook for about 2 minutes, until the onion begins to soften. Add the barley and cook for 3 to 4 minutes. Add the garlic and stir everything for 30 seconds to 1 minute, until the garlic is fragrant.
Add the mushrooms and their juices into the pan, then stir in the vegetable broth and thyme. Raise heat and bring the broth to boil. Reduce the heat a little so that the broth is simmering. Cover the pot, and let the barley cook for 25 to 30 minutes, until the broth has been fully absorbed and the barley is tender. Remove from heat and let the barley sit for 5 minutes.
Stir in the lemon zest and parsley. Season with salt and pepper to taste, and serve.