Heat chicken broth in a large pot over medium-high heat. Add lemongrass and ginger. Simmer 5 minutes, until fragrant.
Reduce heat to retain simmer; add garlic, mushrooms and chile sauce. Cover and cook 5 minutes.
Stir in broccoli, chicken, sweet red pepper and coconut milk. Simmer 5 minutes, until chicken is cooked through. Remove from heat and stir in lime juice and fish sauce. Ladle into bowls and top with scallion, if using.
