Heat the vegetable oil in a large pot over medium-high heat. Add the sliced chicken and cook for 5-6 minutes until lightly browned and cooked through. Remove and set aside.
In the same pot, add the garlic, ginger, and red curry paste. Sauté for 1-2 minutes until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth and coconut milk, stirring to combine with the curry paste mixture. Bring to a gentle simmer.
Add the mushrooms and bell pepper to the pot. Simmer for 8-10 minutes until the vegetables are tender.
Stir in the fish sauce, lime juice, and sugar. Return the cooked chicken to the pot and heat through for 2-3 minutes.
Taste and adjust seasonings as needed. Stir in the fresh cilantro just before serving.
Ladle into bowls and garnish with sliced green onions. Serve hot with extra lime wedges on the side.