Place mushrooms in a ceramic bowl. Combine 2 tbs oil and the sumac in a small bowl. Lightly brush both sides of bread with oil mixture then spoon the rest over the mushrooms, stir to coat.
Preheat barbecue plate on medium heat. Cook flatbread for 2 minutes each side until crisp. Set aside. Increase heat to high, add mushrooms then squeeze over half the lemon and barbecue for 5-6 minutes, turning occasionally until tender. Transfer to a plate, set aside to cool.
Remove the seeds from the cucumber, thinly slice and place into large bowl. Add radishes, green onions, cherry tomatoes, pistachio nuts and mushrooms, season with salt and pepper and toss gently to combine.
Scatter the salad leaf mix over a large platter, spoon over the mushroom salad, break the flatbread into pieces and scatter over the salad with the feta. Drizzle with remaining oil, squeeze over the lemon and serve.