Combine and let stand until the mushrooms are softened, about 20 minutes:
      1/4 ounce dried mushrooms, such as dried porcini mushrooms or dried shiitake mushrooms (about 3 mushrooms per 1/4 ounce)
      1 cup hot water
Remove the mushrooms and squeeze dry with paper towels. Reserve the soaking liquid. Dice the mushrooms finely and reserve. Heat in a soup pot over medium-low heat until the butter is melted:
      1 tablespoon unsalted butter
      1 tablespoon vegetable oil
Add and cook, stirring, until tender but not browned, 5 to 10 minutes:
      5 ounces mushrooms, wiped clean and tough stems removed, coarsely chopped
      1 small leek (white part only), cleaned thoroughly and diced
      1 small onion, diced
      1 medium celery stalk, diced
      1 small carrot, diced
      2 cloves garlic, minced
Increase the heat slightly and add:
      1/3 cup pearl barley
Cook, stirring, until lightly toasted, about 5 minutes. Stir in the reserved diced mushrooms. Strain the soaking liquid through a fine-mesh sieve lined with a dampened paper towel and stir it into the vegetable mixture along with:
      4 cups Brown Beef Stock or Roasted Vegetable Stock
Bring to a boil, reduce the heat, and simmer, partially covered, until the barley is tender, about 40 minutes. Season with:
      1 tablespoon snipped fresh dill
      1/2 teaspoon salt
      1/2 teaspoon ground black pepper
Ladle into warmed bowls and serve immediately.