Heat 1 tablespoon of the oil in a large, wide saucepan over medium heat. Add the butter and barley and toss to coat. Toast, stirring occasionally, until deep golden brown, 8 to 10 minutes. If the farro starts getting too dark, reduce the heat to medium-low. Transfer to a bowl. 

Add another 1 tablespoon of the oil to the pan over medium heat, and add the shallots. Cook for 5 minutes, or until golden. Add half of the mushrooms, increase the heat to medium-high, and cook until browned, 4 to 6 minutes. Add 1 teaspoon salt and pepper to taste. Return the farro or barley to the pan and add the stock and vinegar. Scrape up any browned bits from the bottom of the pan and bring to a boil. Reduce the heat to maintain a simmer, cover, and cook for 35 minutes, or until all the liquid is absorbed. Set aside. 

In a small nonstick skillet, heat the remaining 1 tablespoon oil over high heat. Add the remaining mushrooms and cook, tossing frequently, for about 5 minutes, until browned and crispy. Add the walnuts, ⅛ teaspoon salt, and pepper to taste and cook, tossing, for 3 minutes more.

Stir half of the dill into the pilaf and transfer a serving bowl. Top with the mushroom mixture and the remaining dill and serve.