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.
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 1 1/2 cups.
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.
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.
Fill orange shells with frozen granita mixture and serve immediately.