Cut the chicken into bite sized pieces. Cut the stems off the Thai eggplants and then quarter them. Wash the green beans and then break the ends off. Cut the stems off of the Thai red chili peppers and split them in half. Brush the seeds off and then slice the peppers into thin strips.
Add the quartered eggplants and stir until they are well coated. Add the rest of the coconut milk along with the chicken broth and let simmer for 10 minutes or until the chicken is fully cooked. Add the green beans, 2 tablespoons honey, and 3 tablespoons fish sauce. Stir to mix well. The curry should be salty but with a hint of sweetness. Add more honey or fish sauce to fit your own taste.
Add the chili pepper and kaffir lime leaves and bring to a boil. Add the basil leaves and turn off the heat, stirring to mix in the basil. Serve hot alongside cauliflower or regular rice.