Combine the water and sugar in a medium saucepan and stir over low heat for 5 minutes or until sugar dissolves. Increase heat to high and bring to the boil. Boil for 5 minutes or until mixture thickens. Set aside for 30 minutes to cool.
Meanwhile, place watermelon in the jug of a blender and blend until pureed. Strain puree through a fine sieve into a jug, pressing with the back of a spoon to extract as much liquid as possible (you should have about 600ml of watermelon juice).
Add sugar syrup to watermelon juice and stir until well combined. Pour into an airtight container, cover and place in the freezer for 4-5 hours or until almost set.
Roughly break up the sorbet with a metal spoon and transfer to the bowl of a food processor. Process briefly until sorbet is smooth and has a soft, icy texture.
Return sorbet to container and place in the freezer for a further 4 hours or until firm. Remove from the freezer and repeat step 4. Return sorbet to the container and place in the freezer for a further 5 hours or until firm.
Place the sorbet and egg whites in the bowl of a food processor and process until sorbet is pale and smooth. Return to the container and place in the freezer for a further 4 hours or until almost firm. Scoop into serving glasses or bowls and serve immediately.
