Heat vegetable oil in a large pot or wok over medium heat. Add green curry paste and stir-fry until fragrant.
Pour in half of the coconut milk and bring to a simmer, stirring continuously until a green oil surfaces.
Add chicken thighs and cook until the chicken is seared on all sides.
Add the remaining coconut milk, water or chicken stock, fish sauce, palm sugar, and kaffir lime leaves. Bring to a gentle simmer.
Add Thai eggplant and bamboo shoots. Cook until the eggplant is tender and the chicken is fully cooked.
Stir in red bell pepper, Thai basil leaves, and bird's eye chilies (if using). Cook for another 1-2 minutes until basil wilts.
Taste and adjust seasoning if necessary. Serve hot with steamed jasmine rice.
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