Heat the vegetable oil in a large pot or wok over medium heat until shimmering.

Add the Thai green curry paste and stir-fry for about 2 minutes until it becomes fragrant and slightly darker in color.

Pour in half of the coconut milk and simmer for 3-4 minutes, stirring occasionally, until the oil starts to separate from the milk.

Add the sliced chicken breast to the pot and cook for 3-4 minutes until the meat turns white and is mostly cooked through.

Stir in the remaining coconut milk, chicken broth, bamboo shoots, red bell pepper, and eggplant.

Season the curry with fish sauce and sugar, stirring well to combine all the flavors.

Simmer the mixture gently for 10-12 minutes until the vegetables are tender but still retain a slight crunch.

Tear the kaffir lime leaves directly into the pot and stir to release their citrus aroma.

Turn off the heat and immediately stir in the fresh Thai basil leaves so they wilt slightly but keep their bright green color.

Serve the curry hot over steamed jasmine rice for a complete and comforting meal.