Step 1Clean the mushrooms with a damp paper towel. Trim the stem ends and quarter the mushrooms.
Step 2Put the mushrooms in a tall 8-quart stockpot. Add the dried shiitakes, leek, garlic, thyme and peppercorns. Add 3 quarts (12 cups) cold water. Bring to a boil over high heat. Reduce the heat, cover and simmer 35 minutes.
Step 3Remove the pot from the heat and let stand to cool 5 minutes. Strain through a mesh strainer, gently pressing the vegetables with a spoon to extract juices. Discard the vegetables. You should have 11 cups of broth; add water until the broth measures 11 cups, if needed.
Step 1Heat 2 tablespoons oil in a tall 8-quart stockpot over medium-high heat. Add the onion, carrot and celery and saute until the vegetables are tender but not browned, about 4 minutes. Add the garlic and cook 1 minute.
Step 2Stir in the barley and stock. Bring the mixture to a boil. Reduce the heat to simmer and cover. Cook 1 hour, stirring occasionally.
Step 3Heat 1 tablespoon oil in a medium nonstick skillet until hot. Add the mushrooms and saute until lightly browned, about 7 minutes. Add the salt, Swiss chard, turnips and sauteed mushrooms to the stockpot. Bring the soup to a simmer, cover and cook 30 minutes.