Warm the vegetable oil in a large skillet or wok over medium heat. Add the green curry paste and cook for 1–2 minutes, stirring continuously, until the aroma becomes vibrant and intense.
Add the chicken to the pan, ensuring each piece is thoroughly coated in the paste. Sauté for 3–4 minutes, allowing the chicken to lightly sear and absorb the flavors.
Pour in the coconut milk, mixing well to combine with the curry paste. Allow the mixture to come to a gentle boil, then reduce to a simmer for 5 minutes to deepen the flavor.
Incorporate the diced eggplant, trimmed green beans, and bamboo shoots, if using. Let the curry simmer for 7–10 minutes, or until the vegetables are tender but still vibrant in color.
Season the curry by adding fish sauce and sugar, stirring to blend. Adjust the flavor as needed, balancing the saltiness and sweetness to your liking.
Introduce the sliced red chilies, stirring gently into the curry. Let it cook for an additional 2 minutes, ensuring the spices meld perfectly.
Top with fresh Thai basil leaves for a fragrant finish. Serve immediately alongside steamed jasmine rice or rice noodles, and garnish with lime slices for a zesty touch, if desired.