Cut the tops and bottoms off the eggplant and cut into quarters.
Thinly slice the chicken breast crosswise. Set aside.
Prepare the green curry paste. In a large skillet over medium heat, toast the cumin seeds and coriander seeds until golden and fragrant, about 2-3 minutes. Transfer to a pestle or bowl.
Add the salt and pound with a mortar until the spices are broken up. Continue pounding as you add the white peppercorns, lemongrass, kaffir lime peel, galangal, garlic, Thai green chilis, cilantro stems, Thai basil, kaffir leaves, shallots, and shrimp paste, until a coarse paste forms.
Heat a medium skillet over medium heat. Add vegetable oil, 2 tablespoons of green curry paste, and 3 tablespoons of basil oil (if using).
Add a splash of the coconut milk, stirring until it forms a paste.
Add the sliced chicken breast, the rest of the coconut milk, and the eggplant.
Season with the fish sauce and sugar. Increase the heat to medium high and bring to a boil. Once boiling, cook for 2-3 minutes.
Stir in the bamboo shoots, kaffir leaves, and red bell pepper, cooking for 3-4 minutes until bell peppers have slightly softened.
Add the Thai basil. Remove the curry from the heat and serve with white rice.