Soak the dried chickpeas in cold water for 8 hours, then drain.
Combine chickpeas, carrot, and onion in a medium saucepan, add 4 cups water, and bring to a boil.
Reduce the heat and simmer until the chickpeas are tender, about 1 1/2 hours.
Drain, remove carrot and onion, reserving 1 cup of the cooking liquid.
Meanwhile, preheat the oven to 300°F.
Toss the garlic and eggplant with 1.4 cup of olive oil and arrange on a cookie sheet (eggplant with the cut side down) and roast for 40 minutes.
Add the chilies to the roasting pan, cut side down and roast for another 10 minutes. Set aside until cool enough to handle
Scoop the flesh from the eggplant and transfer to a blender and then add the roasted garlic and chilies, chickpeas, harissa, cumin, remaining 2 tbsp olive oil, and 2-3 tbsp of the reserved cooking water.
Puree, adding more of the cooking liquid 2-3 tbsp at a time if necessary until it's smooth and creamy.