Position a rack in the top third of the oven and preheat to 450 degrees F. Line a rimmed baking sheet with parchment paper.
Lay the lemon slices in an even layer on one side of the baking sheet. Place the chicken thighs skin-side up on top of the lemon slices and brush with 1 tablespoon olive oil. Sprinkle the chicken thighs with berbere, chili powder, ground cumin, and some salt and pepper. Place the carrots in the center of the baking sheet (leaving an empty space on the other side) and drizzle with 1 tablespoon olive oil, the za'atar and some salt. Toss to coat and top with the whole cinnamon stick.
Roast until the carrots are almost completely tender and the chicken thighs are crispy on top and almost cooked through, 40 minutes. Remove the baking sheet from the oven and add the chickpeas to empty space, tossing with the remaining 1 tablespoon olive oil and some salt and pepper; spread into an even layer.
Roast until the chicken has brown, crisp skin and reads an internal temperature of 160 degrees F, the carrots are completely tender and browned in spots, and the chickpeas are warmed through, about 5 minutes more. Discard cinnamon stick. Divide the chicken and vegetables between two plates and serve with the pan juices drizzled over.
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