Add oil to a heavily basked skillet or dutch oven and heat over medium-high heat.
Add curry paste, garlic, and ginger. Stir to mix and cook for 2-3 minutes.
Add the chicken broth and coconut and mix to combine. Add fish sauce, sugar, and kaffir lime leaves if using and stir. Bring to a simmer.
Add chicken, stir and then lower the heat so it is gently bubbling. Cook 7 minutes, stirring periodically.
Add bell pepper and cook for four minutes. Then add eggplant and cook for an additional four minutes or until soft. Taste the sauce and adjust with fish sauce or sugar to preference.
Stir in basil and lime juice. Note the sauce will be thin, but that is intended as it will darken.
Serve over rice with desired garnishes.