To make the curry paste, place all of the paste ingredients in a food
processor and process until a smooth consistency. Set aside.
Prepare the kaffir lime leaves by tearing the leaf away from either side of the stem. Discard central stem. Using scissors, cut the leaves into thin strips. Set aside.
Warm a wok or large skillet over medium-high heat. Add oil and swirl around, and add the green curry paste. Stir-fry briefly to release the fragrance, 30 seconds to 1 minute.
Reserve 1 tablespoon per serving of coconut milk to use later, and add the remaining coconut milk to the wok.
Add chicken, stirring to incorporate. When the curry sauce comes to a boil, reduce heat to medium or medium-low and simmer 5 minutes, or until chicken is cooked through. Stir occasionally.
Add the vegetables, plus strips of a lime leaf (or lime zest), stirring well to incorporate. Simmer until vegetables are cooked to your liking. Do a taste-test.
Serve with Thai jasmine rice on the side, allowing guests to add their own. Top each portion with fresh basil, then drizzle 1 tablespoon of reserved coconut milk over each.