Score the duck skin in a crosshatch pattern. Pan-sear duck breasts skin-side down until fat renders and skin becomes crispy.
Transfer duck to preheated oven and cook for 8 minutes. Remove and let rest before slicing.
Heat oil in a large pan or wok over medium heat. Add curry paste and fry until fragrant, about 2-3 minutes.
Add the thick coconut cream and cook until oil begins to separate from the mixture.
Stir in palm sugar, fish sauce, and kaffir lime leaves. Mix well to combine.
Add remaining coconut milk, pineapple chunks, and lychees or grapes. Simmer for 4-5 minutes.
Add sliced duck to the curry and heat through gently for 2-3 minutes.
Taste and adjust seasoning as needed. Stir in fresh Thai basil leaves just before serving.