Heat vegetable oil in a large skillet or wok over medium heat.
Add chicken pieces and cook until lightly browned.
Remove chicken from the pan and set aside.
In the same pan, sauté onion until soft.
Add garlic and ginger and cook for 30 seconds.
Stir in red curry paste and cook for 1 minute to release flavor.
Pour in coconut milk and stir until well combined.
Add bell pepper and carrots to the sauce.
Return chicken to the pan and mix well.
Season with fish sauce, brown sugar, salt, and black pepper.
Simmer for 15 minutes until chicken is fully cooked and sauce thickens.
Stir in lime juice and garnish with fresh cilantro before serving.