Place barley in heavy large saucepan. Cook over medium heat until pale golden, shaking pan occasionally, about 10 minutes. Add broth to pan and bring to boil. Reduce heat to medium-low, cover and simmer until barley is tender and broth is absorbed, about 35 minutes. Uncover and let barley cool. Char poblano and red bell pepper over gas flame or in broiler until blackened on all sides. Enclose in paper bag and let stand 10 minutes. Peel, seed and dice poblano and red bell pepper. Place barley, poblano and red bell pepper in large bowl. Add tomatoes and next 5 ingredients; toss to blend. Season salad with salt and pepper. (Can be prepared 1 day ahead. Cover; refrigerate. Bring to room temperature before serving.)
Prepare barbecue (medium-high heat). Spray mushrooms with nonstick spray; sprinkle with salt and pepper. Grill until cooked through, about 4 minutes per side. Transfer to work surface; slice thinly. Arrange 6 spinach leaves on each of 4 plates. Top with barley salad. Arrange 1 sliced mushroom alongside each salad. Serve while mushrooms are still warm.