Empty the oranges by scooping out their flesh.
Drain them by turning them over on a clean cloth. Set aside.
Chop the pulp in a food processor to obtain a puree.
Mix it with sugar and bring to a low boil for 10 minutes.
Pass the mixture through a sieve to remove the pulp. Let it cool completely. Start churning in an ice cream maker.
Incorporate the Italian meringue at the end of churning.
For serving, fill the oranges with sorbet; replace the orange top and place in the freezer for 2 hours before serving.