In a small bowl, stir together the ground cumin, cayenne pepper, ground cinnamon and kosher salt. Evenly coat the chicken with half of the spice mixture. Reserve the remainder.
Quarter the squash lengthwise. Remove the seeds and slice into 1/2-inch-thick slices. Toss with 2 tablespoons olive oil and salt to taste.
Heat remaining 2 tablespoons olive oil in the buffet casserole or shallow cast iron pan over medium-high heat. Once the oil is hot, place the chicken thighs skin side down and cook until crisped and golden, about 5 minutes. Flip the thighs over and sear the bottom side, about 2 minutes. Remove the chicken from the pan and set aside.
Add squash to the pan in an even layer. Cook until browned, about 2 minutes on each side. Remove from the pan and set aside.
Lower the heat to medium-low. Add cumin seeds, coriander seeds and chickpeas. Stir frequently until the seeds are fragrant and some of the coriander seeds begin to pop. Add the coconut milk, remaining ground spice mixture, cinnamon stick and lime leaves. Stir to combine and bring to a simmer.
Return the squash and chicken thighs to the pan. Cover and cook 20 minutes or until the squash is tender and the chicken is cooked through. Taste and season with additional salt if needed. Garnish with fresh cilantro sprigs.