Put a baking sheet on the middle oven rack and preheat to 450˚. Pat the chickpeas dry with paper towels; toss with the carrots, 2 tablespoons olive oil, 2 pinches of salt and a few grinds of pepper in a large bowl. Spread on the hot baking sheet and roast, stirring halfway through, until the chickpeas are browned and crisp and the carrots are tender, 30 to 35 minutes. Sprinkle with 1 1/2 teaspoons za’atar and toss to coat. Let cool slightly.
Meanwhile, stir the vinegar, honey, shallot, 1/2 teaspoon salt and a few grinds of pepper in a large bowl; let sit 10 minutes. Gradually whisk in the remaining 1/4 cup olive oil.
Remove the carrots to a cutting board and cut into 2-inch pieces; transfer to the bowl with the dressing. Add the chicken, mesclun, snap peas, parsley and feta. Season with salt and pepper and toss gently. Top with the roasted chickpeas and sprinkle with more za’atar.