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.
In a large deep skillet over medium heat, pour 1.5 cups of coconut milk and however much Thai green curry chili paste you decide to use. You can always add more later, so start with a little at first (2 or 3 tablespoons) and then keep adding paste if you want more flavor and spice.
Mix the coconut milk and curry paste together well and stir continuously to prevent sticking and burning. Let simmer for 5 minutes.
Add the chicken pieces and stir to coat, cooking for 2 minutes or until it is partially cooked.
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.