In a 2 qt. saucepan, bring 4 cups of water to a boil, add the dried mushrooms. Remove from heat and cover, let soak for 20 minutes. Strain the mushrooms through a fine mesh strainer over a bowl to remove any sediment and dirt, reserving the liquid. Finely chop the mushrooms and set aside.
In a 6-3/4 qt. dutch oven or soup pot, heat the olive oil over medium-high heat. Add the onions and a pinch of salt, stirring for about 4 minutes. Add the fresh mushrooms, carrots, celery, and 1/2 teaspoon of salt, stir and cook the vegetables for about 5-6 minutes or until tender. Add the garlic and thyme, stir to combine.
Add the wine to deglaze the pot, stirring until the liquid is reduced by half, about 2-3 minutes. Add the soaked chopped dried mushrooms, reserved mushroom liquid, broth, barley, 1/2 teaspoon salt and black pepper. Bring to a simmer and then reduce heat and cook for about 45 minutes or until the barley is tender.
To serve; garnish with parsley and Parmigiano-Reggiano.