In a 3-1/2- to 5-quart slow cooker combine the chicken, broth, carrots, onion, ginger, garlic, lemongrass, and crushed red pepper.
Cover and cook on low-heat setting for 6 to 7 hours or on high-heat setting for 3 to 3-1/2 hours. If necessary, skim off fat. Stir coconut milk, sweet pepper, mushrooms, and cilantro into chicken mixture. Cover; let stand 5 to 10 minutes. Discard lemongrass (if using). Ladle soup into bowls. Sprinkle peanuts over each serving. Makes 6 servings.