In a blender, combine all of the ingredients. Add a splash of water to help it blend easily. Blend until well mixed to a fine texture. Cook the paste in the oil until the paste is well cooked, about 7 to 10 minutes.
Into a large saucepan over medium heat, add cooking oil and red curry paste and stir well. Add half of the coconut milk and gently stir. Add the duck, apple eggplant, pea eggplant, tomatoes, pineapple, and lychee. Bring to a boil and cook uncovered until vegetables are tender. Add the fish sauce and sugar to desired sweetness. Remove from heat and add the chili, basil, kaffir lime leaves and serve.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.