Step 1Toast the farro in a dry medium saucepan over medium heat until it smells nutty and turns golden, about 5 minutes. Add the water and bring to a simmer. Season with one-half teaspoon salt and cook until the farro is tender, about 45 minutes. Drain (there will probably still be some liquid left), rinse in cold running water and gently pat dry in a kitchen towel. Place in a mixing bowl, add more salt if necessary, and set aside. (The dish can be prepared to this point up to a day ahead and refrigerated tightly covered.)
Step 2Trim the dried ends of the mushroom stems and quarter the mushrooms lengthwise. Heat the oil in a medium skillet over medium-high heat, and when it's very hot, add the mushrooms and sprinkle with one-half teaspoon salt. Cook, tossing frequently, until the mushrooms give up their moisture, 3 to 4 minutes. Add the garlic and keep cooking, continuing to toss to prevent scorching, until the mushrooms are dry, another 3 to 4 minutes.
Step 3Add the mushrooms to the cooked farro, along with 2 tablespoons chopped dill, the walnuts and green onions. (The dish can be prepared to this point up to 4 hours in advance and refrigerated tightly covered; bring to cool room temperature before serving.)
Step 4When ready to serve, stir in the red wine vinegar and toss to combine. Adjust the seasoning, adding more salt and more vinegar as needed. Mound the grain mixture on a platter. Arrange the red pepper strips casually across the top. Sprinkle with the crumbled feta and then the remaining chopped dill and serve. This makes about 4 cups of salad.