Bring a tea kettle, with 3 cups of water, to a boil over medium heat.
In a heatproof bowl add the sugar, ginger and tea bags. Pour in 3 cups of boiling water. Stir to dissolve the sugar and let the tea bags steep until the liquid is cool. Strain and pour into an 8 by 8-inch metal cake pan and put it into the freezer. Check it after 45 minutes to 1 hour (depending on your freezer). Stir with a fork breaking up any ice crystals that have formed. Put the pan back into the freezer and continue checking and forking every 45 minutes to 1 hour until you have a container of ice shards.
To make orange cups, slice the oranges in half and carefully remove the flesh with a spoon, making sure to keep the rinds intact. In a small bowl, muddle the orange flesh to get out the juice, then strain and reserve it for the "Rising Sun" cocktail recipe. Slice a bit of the bottom of each orange half so that it can stand upright. Put the orange rinds into the freezer.
Once the granita is completely frozen, divide it evenly among the 4 orange halves and serve immediately.