Put the purple yam in a small mixing bowl and place the bowl in a steamer. Steam the yam covered over boiling water for 30 minutes. Remove the purple yam from the steamer and immediately add the glutinous rice flour. Mash the purple yam together with the glutinous rice flour to create a flakey starch mixture. Add the boiling water and mix well. A soft dough should form at this point.
Pinch about ½ teaspoonful of the dough and roll it into a ball about ½ inch in diameter. Continue to form dough balls until the dough if completely used up. There should be about 60 balls.
Combine all the ginger syrup ingredients together in a saucepan. Bring the liquid to a boil then turn the heat o medium low and simmer for about 30 minutes. Discard the ginger slices and reserve the syrup.
Bring a pot of water to a boil and turn the heat to medium. Drop all the mochi balls into the boiling water and let cook for about 15 minutes or until all the balls float to the top. Drain the mochi balls and add them to the ginger syrup and serve hot.