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.
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.
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