In a deep, medium skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Add the carrots and cook until slightly softened, 3 to 4 minutes. Add the chicken, figs and cinnamon and toss. Stir in half of the chicken broth, then the rice and warm through, 3 to 4 minutes. Stir in more broth, as needed, to make a slightly soupy mixture.