Position a rack in the top third of the oven and preheat it to 400 F. Line a sheet pan with parchment paper.
Dry the chickpeas well before adding them to a food processor. Pulse until they resemble coarsely ground bread crumbs, loosening them with a fork as necessary so you don't form a paste. Spread these out evenly on the lined sheet pan and drizzle all over with 3 tablespoons olive oil (you want them pretty covered). Season with the za'atar and ½ teaspoon salt. Gently mix until everything is evenly coated.
Roast the chickpeas until they are golden and dry, 20 to 25 minutes, shaking and stirring with a spatula halfway through to help them crisp up.