Combine persimmon puree, granular sugar, dark rum and sea salt in a blender and puree until smooth.
Combine heavy cream, powdered sugar, and vanilla extract in a mixer bowl and whip until it reaches the soft peak stage.
Layer the persimmon puree and whipped cream in serving bowls and stir to mix. Put in fridge to chill until ready to serve.
note* You may have to adjust the amount of sugar you add depending on the sweetness/ripeness level of the Persimmons.