Preheat oven to 375°F. Pat chickpeas dry with a paper towel and toss with 1 tablespoon olive oil. Spread evenly onto a baking sheet and roast for 30-35 minutes, or until golden and crispy. Sprinkle with za’atar.
Meanwhile, heat a cast iron skillet over medium-high heat and add remaining tablespoon olive oil. Add garlic and cook for 30 seconds, or until toasted and fragrant. Add Brussels sprouts and cook until slightly wilted, about 3 minutes. Stir in lemon zest and 2 tablespoons lemon juice and transfer mixture to a large bowl.
Place pita wedges on a baking sheet and toast until crisp, about 6-8 minutes.
Make the dressing: Whisk together tahini, remaining lemon juice, honey and salt until smooth.
Stir dressing into Brussels sprouts and top with chickpeas. Serve with pita and garnish with parsley, if desired.