Peel persimmon, remove the stem and leaves, and discard. If there are seeds, remove and discard. Cut the persimmon flesh into small pieces and put into a blender with coconut milk and frozen dessert. Blend until smooth.
Divide the mixture equally into 2 serving cups or glasses. Tap the bottom of each cup to get any bubbles out. Refrigerate for about 2 hours until set.
In the meantime, toast the coconut flakes in a non-stick skillet over medium-low heat until golden brown. Let cool.
When the puddings are set, sprinkle with the coconut flakes over the top. If there is any liquid on top, discard it before adding coconut. Serve immediately.