In a large deep saucepan, heat the oil over medium heat until shimmering.
Add the onions, mushrooms, eggplant and green curry paste and stir fry for a minute or two until fragrant.
Add 1 cup of coconut milk to the pan and bring to a boil. Add chicken and onions and simmer over medium heat for 5 minutes.
Add in the remaining coconut milk, fish sauce, and palm sugar. Add in 1/2 cup water if the mixture looks too dry. Simmer gently for 15 minutes until vegetables soften.
Add in the green beans and kai lan, and simmer for an additional 5 minutes until cooked through and vegetables are bright green.
Serve with lime wedges, cilantro, Thai basil and hot jasmine rice.