Heat oil in a large pot or Dutch oven over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and red curry paste and cook for 1 minute more, stirring constantly.
Pour in chicken broth and coconut milk. Bring to a simmer. Stir in fish sauce and brown sugar.
Add shredded chicken, mushrooms, and red bell pepper. Simmer for 10-15 minutes, or until vegetables are tender.
Stir in lime juice. Garnish with cilantro and serve.