Preheat the oven to 375 degrees F. Coat a 9-by-13-inch pan with cooking spray.
Evenly scatter the chicken, broccoli, rice, red pepper and onion in the pan. In a bowl, whisk together the coconut milk, broth, curry paste, fish sauce, brown sugar and lime juice. Pour the mixture over the ingredients in the pan. Bake until the rice is cooked and most of the liquid is absorbed, 45 to 50 minutes. Sprinkle with the chopped peanuts and cilantro before serving.