Heat the oil in a large pot over medium-high heat. Add the spaghetti and cook, stirring, until lightly toasted, about 2 minutes. Add the carrot, garlic, cumin, cinnamon and half of the cilantro; cook, stirring, until the spices are toasted, about 1 minute. Add the broth, chickpeas, tomatoes, 1 cup water, and salt and pepper to taste. Cover and bring to a simmer, then reduce the heat to medium low and cook until the spaghetti is just tender, about 8 more minutes.
Season the chicken with salt and pepper and add it to the soup. Simmer until cooked through, about 2 minutes. Add the remaining cilantro and season with salt and pepper.