In a large skillet or wok, heat the vegetable oil over medium heat. Add the chicken pieces and cook until browned, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced onion, garlic, and ginger. Sauté for about 3-4 minutes until the onion is translucent.
Stir in the Panang curry paste and cook for an additional 1-2 minutes, allowing the flavors to meld.
Pour in the coconut milk, fish sauce, and brown sugar. Stir well to combine, then bring the mixture to a gentle simmer.
Return the cooked chicken to the skillet, along with the sliced bell pepper and green beans. Simmer for about 10 minutes, or until the chicken is cooked through and the vegetables are tender.
Remove from heat and stir in the lime juice. Adjust seasoning if necessary.
Serve hot over cooked jasmine rice and garnish with fresh basil leaves.