Heat the vegetable oil in a large skillet over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic and grated ginger, cooking for an additional minute until fragrant.
Add the chicken pieces to the skillet, cooking until they are no longer pink, about 5-7 minutes.
Stir in the Panang curry paste, ensuring the chicken is well coated.
Pour in the coconut milk, fish sauce, and brown sugar, stirring to combine. Bring the mixture to a gentle simmer and cook for 10 minutes, allowing the flavors to meld.
Add the sliced red bell pepper and green beans to the skillet, cooking for an additional 5 minutes until the vegetables are tender but still crisp.
Remove from heat and stir in the lime juice. Serve hot, garnished with fresh basil leaves.