Ingrid Hoffmann's Orange Granita

Cut the top off each orange, just enough so you can scoop out the pulp. Discard tops and scoop all the pulp into a colander or fine mesh strainer set over a bowl. Put the empty orange shells in the freezer and freeze for at least 2 hours or up to a day. Mash the orange pulp in the colander to remove as much juice as possible. Add extra juice if necessary to reach 11/2 cups. Discard pulp. Combine 1/2 cup water with the sugar in a small saucepan and bring to a boil. When the sugar is totally dissolved, remove from heat and let cool. Stir in orange juice and orange liqueur, if using. 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.