Combine barley and 2 1/2 cups water in a bowl; cover and let soak overnight. Combine dried mushrooms and 1/2 cup water in a bowl; cover and let soak overnight.
Place the chuck roast in a large stockpot over medium heat; cover the roast with 5 quarts water. Bring the water to a boil, skimming any foam off the surface. Boil the roast until the foam no longer forms on the water, about 15 minutes. Pour the barley, mushrooms, and the water from both bowls into the stockpot; stir in the parsley, dill, broth, salt, and pepper. Return the mixture to a boil; reduce heat to low; simmer, stirring every hour, until soup has reduced to desired thickness, 4 to 6 hours.
Remove large pieces of beef from the soup; trim and discard fat. Cut remaining meat into bite-sized pieces and return them to the soup.