Halve the melons across their width. Scoop out the seeds and remove the flesh from one melon. Purée it in a food processor. Transfer to a small saucepan, add the star anise, caster sugar, and cinnamon sticks (broken in half). Simmer gently over low heat for 10 minutes. Cool and refrigerate.
Use a melon baller to scoop balls from the second melon.
Preheat the oven to 180°C (thermostat 6).
For the shortbread: In a food processor, blend the icing sugar, 50 g soft butter, flour, egg, and cinnamon powder until the dough forms a ball. Roll out on a floured work surface and cut into biscuits.
Bake on a buttered baking sheet for 15 minutes. Allow to cool.
Fill the melon halves with the chilled purée, garnish with melon balls, spices, and mint sprigs. Refrigerate until serving.
Enhance visual appeal by pairing an orange-fleshed melon with a green one (such as watermelon).
