Have the stock at a simmer. Heat the oil in a heavy wide pan or soup pot. Add the onion and garlic and cook over medium heat until the onion is translucent, about 4 minutes. Add the barley and cook for 1 minute, stirring to coat the grains. Raise the heat a little, add the wine, and cook, stirring frequently until the wine is nearly absorbed. Add 2-1/2 cups of the stock, cover the pot, and simmer until the stock is nearly absorbed. Now start adding stock 1/2 cup at a time, stirring more or less constantly and waiting for each addition to be absorbed before adding more. After about 40 minutes the barley should be tender and the dish thick and creamy. You may not need to use the full amount of stock. Stir in the butter, cheese, half the parsley, and lemon juice to taste. Taste for salt and season with pepper. Serve garnished with the remaining parsley.