Cook the tortellini as instructed on package. Drain and set aside.
Dice the cucumbers, peppers and red onion and add them to a large salad bowl with the tortellini, chickpeas, sliced olives and parsley.
Prepare the lemon za'atar dressing by combining all of the dressing ingredients together in a small bowl or jar, and whisk or shake together until evenly incorporated.
Pour the dressing over the tortellini salad and toss to combine. Serve cold or at room temperature.