Heat the oil in a wok or pot over medium-high heat. Add the green curry paste and cook, stirring constantly with a wooden spoon, until the mixture becomes dry and fragrant, about 3 minutes. Add the coconut milk, stir to combine, and simmer until the liquid reduces by half, 7 to 10 minutes. Add the chicken and stir, for 1 to 2 minutes, then stir in the chicken broth, fish sauce, and sugar. Add the eggplant, reduce the heat, and simmer until the chicken is cooked and the eggplant is tender, 5 to 7 minutes. Add the kaffir lime leaf, chopped basil, and bell pepper, bring to a boil, and remove from heat. Transfer to two bowls, garnish each with a basil sprig, and serve.