Preheat the oven to 425°F. Toss the chopped carrots and whole garlic cloves with 2 tablespoons of olive oil. Scatter evenly on a baking sheet lined with parchment and roast in the oven until the carrots are tender and lightly browned, 18 to 20 minutes.
In the bowl of a food processor, combine roasted carrots, roasted garlic, chickpeas, tahini, lemon juice, water and all of the spices. With the motor running drizzle in the remaining 2 tablespoons of olive oil. Whirl away until smooth, scraping the sides down as necessary. Taste and adjust seasonings if necessary. If the hummus is too thick, add a little more water or oil and process until desired consistency is achieved.