In a medium heavy saucepan, combine the sugar, water, ginger, cinnamon stick, and cardamom pods and bring to a boil over medium heat, stirring to dissolve the sugar. Reduce the heat and simmer gently for 30 minutes. Remove from the heat and let cool to room temperature.
Set a fine-mesh sieve over a bowl and pour the syrup through the sieve. Put the cinnamon stick in a jar and discard th