Prepare a grill for medium high heat; thoroughly clean grates and brush with oil. Toss carrots, 3 tablespoons harissa, half of the garlic, thyme, cumin and 1 teaspoon salt together in a medium bowl. Lay out a 12" sheet of heavy duty foil and scrape carrot mixture into the center. Fold over the sides and form a tight seal. Grill foil pack, turning once, until carrots are tender and lightly charred, 30-45 minutes. Keep wrapped and let cool slightly.
Puree chickpeas, reserved liquid and tahini in a food processor until smooth and thick. Add remaining 1 tablespoon harissa, remaining garlic, 2 tablespoons olive oil, cooled carrots and accumulated juices, lemon juice and 2 teaspoons salt and puree until smooth. With the motor running, drizzle in the remaining 2/3 cup oil and continue to process until creamy; adjust seasoning if necessary.
Transfer to a serving bowl, top with additional harissa, olive oil, thyme leaves and Aleppo pepper.