Season the chicken generously on all sides with salt and pepper.
In a large pot, heat the oil over medium-high heat. Cook the chicken for about 5 minutes, until it begins to brown and releases easily from the pan.
Flip the chicken over and cook the other side for an additional 5 minutes until browned. Transfer the chicken to a plate and set aside.
Add the carrots and bell pepper to the same pot. Sauté for about 3 minutes, until slightly softened.
Stir in the garlic, ginger and curry paste and cook for another minute until fragrant.
Stir in the broth, coconut milk, fish sauce, brown sugar and rice. Bring mixture to a simmer.
Return the chicken to the skillet. Reduce the heat to medium-low, cover and cook for 15 to 20 minutes, until all of the liquid is absorbed and the chicken has reached an internal temperature of 165ºF (74ºC).
Stir in the lime juice and serve warm, garnished with optional toppings if using.