In a small bowl, whisk together ½ cup (120ml) coconut milk and ½ cup (120ml) water; set thinned coconut milk mixture aside. Remove and discard the mid-rib from the makrut lime leaves; set 8 of the leaves aside. Stack remaining 2 makrut lime leaves, fold in half widthwise, then slice into hair-thin strips; set aside separately.

In a 3-quart saucepan, combine coconut oil with ½ cup (120ml) coconut milk and bring to a simmer over medium heat. Cook, stirring often with a rubber spatula, until thickened slightly, about 1 minute.

Add curry paste, stir vigorously to combine, and use a rubber spatula to scrape sides of the saucepan to fully incorporate paste. Raise heat to medium-high and cook, stirring and scraping constantly until paste mixture begins to spit, about 1 minute. Lower heat back to medium, and continue to cook while gradually adding remaining ½ cup (120ml) coconut milk in 2-tablespoon (30ml) increments, until paste darkens slightly and the fat begins to separate from curry paste, 5 to 6 minutes.

Add fish sauce and palm sugar, and stir until palm sugar is fully dissolved, about 30 seconds. Lightly season chicken on all sides with salt, add to saucepan with reserved whole makrut lime leaves, and stir to evenly coat with curry paste mixture. Add reserved thinned coconut milk mixture and bring to a simmer. Cook, stirring occasionally, until chicken is cooked through and tender and liquid has thickened slightly, about 10 minutes.

Add eggplants, and continue to cook, adjusting heat as needed to maintain a simmer, until eggplants are just cooked through but still have some bite to them, about 3 minutes. Remove from heat, add sweet basil, and stir until wilted and incorporated.

Transfer curry to a large serving bowl or divide between individual bowls, and garnish with reserved thinly-sliced makrut lime leaves. Serve with cooked jasmine rice.