1) Cut the top off each orange, just enough to scoop out the pulp for later use. Discard tops and freeze empty orange shells.
NOTE: For easier scooping, roll the oranges by hand before cutting the tops, using a firm downward pressure to loosen the pulp.
2) In a colander, fine mesh strainer, or food mill, mash the orange pulp to remove as much juice as possible. Add additional juice, if necessary, to make 360ml.
3) Combine water and sugar in a small saucepan and bring to a boil. When the sugar is totally dissolved, remove from heat and allow to cool. Add orange juice and orange liqueur.
4) Pour the mixture into a shallow glass dish and place level in the freezer for 2 to 3 hours, mixing gently with a fork every 20 minutes until it forms ice crystals and thickens. The frequent mixing will keep the granita from freezing into a solid block.
5) Fill orange shells with frozen granita mixture and serve immediately.