Heat a little vegetable oil in a pan over medium heat. Add the red curry paste and stir-fry until fragrant. Add about half of the coconut milk and stir until well combined.

Add the chicken and stir-fry. Pour in the chicken broth and mix well. Bring to a boil, then reduce the heat to low. Simmer for about 10 minutes until the chicken is tender and the flavors are absorbed.

Add the kaffir lime leaves. Season with fish sauce and sugar. Pour in the remaining coconut milk and stir to combine. Taste and adjust seasoning as desired.

Add the eggplant, then the sliced red chili peppers. Bring to a boil again. Add the Thai basil leaves, stir to combine, then remove from heat. Serve hot in a bowl.