Bring a large pot of water to boil over high heat. Add chickpea pasta, reduce heat to maintain a lively simmer and cook, undisturbed, until tender, 6 to 7 minutes. Drain and rinse with cold water. Transfer to a large rimmed baking sheet; spread in an even layer. Allow to cool at room temperature for 10 minutes.

Meanwhile, whisk together the olive oil, lemon juice, za’atar, thyme, cumin, garlic powder, salt, and pepper in a large serving bowl.

Add the sliced cucumber, halved tomatoes, rinsed chickpeas, chopped roasted red peppers, sliced red onion, mozzarella pearls, and the cooled pasta; toss to combine.

Garnish with additional za’atar, thyme, and pepper, if desired.