For the curry duck: Heat the oil in a 12-inch wok over moderately high heat until hot but not smoking. Add in the curry paste, kaffir lime leaves and coconut milk. Bring to a boil and then let it simmer a few minutes, stirring occasionally, until fragrant.
Add 2 cups water, the fish sauce, cane sugar and shrimp paste and simmer, stirring occasionally, until slightly thickened, about 5 minutes. Stir in the bamboo, basil, eggplants, string beans, cooked duck breast and bell peppers and simmer for about 5 more minutes. Divide the curry among 4 bowls and serve immediately with rice.