Heat the oil in a large pot over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, garlic, and ginger to the pot. Stir and cook for 2 minutes until the onion softens.
Stir in the curry paste and cook for 1 minute until fragrant.
Add the rinsed jasmine rice, coconut milk, chicken broth, fish sauce, and brown sugar. Stir everything together.
Bring the mixture to a gentle boil, then reduce the heat to low. Cover the pot and simmer for 15 minutes.
Remove the lid and stir in the sliced red bell pepper. Cover again and cook for 5 more minutes until the rice is tender and the liquid is absorbed.
Turn off the heat. Stir in the lime juice, then let the pot sit covered for 5 minutes.
Fluff the rice with a fork and top with chopped cilantro and green onions before serving.