Bring 1 cup water and sugar to a boil, stirring until sugar is dissolved. Boil 3 minutes, then cool. Put fruit chunks into blender and purée with lemon juice until smooth. Add sugar syrup and blend. Chill until cold, at least 2 hours.
Freeze mixture in an ice-cream maker.
To Serve
Cut profiteroles in half and fill with cinnamon persimmon sorbet. For a fifty-fifty dessert fill half with persimmon sorbet and half with vanilla bean ice cream. Sorbet may be made 4 days ahead.
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