Pour 3 cups boiling water over the bulgur in a large bowl. Cover tightly with plastic wrap and let sit until tender, about 20 minutes. Drain and let cool.
Meanwhile, make the dressing: Whisk the lemon zest and juice, vinegar, oregano, sugar and a pinch each of salt and pepper in a large bowl until smooth. Slowly whisk in the olive oil. Add the cucumbers, tomatoes, red onion and olives; season with salt and pepper and toss. Let sit 20 minutes.
Add the bulgur, feta, mint and parsley to the vegetables. Season with salt and pepper and toss. Top each serving with the pepperoncini.