In a large, deep skillet, heat the olive oil. Add the shallots and garlic and cook over moderately high heat, stirring constantly, until softened, about 5 minutes. Add the mushrooms and thyme and season with salt and pepper. Cook, stirring frequently, until tender, about 8 minutes. Add the barley and cook, stirring, for 1 minute. Add the wine and cook until absorbed, about 5 minutes.
Add 1 cup of the hot beef broth mixture to the barley and cook over moderate heat, stirring frequently, until nearly absorbed. Continue adding the hot broth, 1 cup at a time and stirring frequently, until the barley is al dente, about 35 minutes. Season with salt and pepper and transfer to a bowl. Garnish with chives and the cheese shavings and serve.