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Preheat oven to 400 degrees.
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In a large serving bowl, whisk together all the dressing ingredients except the olive oil. While whisking constantly, pour the oil in as a steady stream until combined. Add chickpeas and toss well. Set aside.
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On a rimmed cookie sheet, toss the carrots, chicken breast, garlic, cumin, and oil until well-combined. Sprinkle evenly with the salt. Roast, until carrots are fork-tender and chicken is cooked through, about 25 minutes, stirring occasionally.
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Remove the garlic from the pan and chop them into very small pieces. Shred the chicken. Add the garlic, chicken, carrots and any pan juices to the chickpeas and stir to combine.
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Cool slightly, then add the remaining ingredients, seasoning with salt to taste.
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Serve warm or at room temperature.