Combine the water, sugar, 1 tablespoon of the ginger, cloves, cardamom and a big pinch of pepper in a medium saucepan. Bring to a boil, stirring until the sugar dissolves. Add the cranberries and bring to a boil. Reduce the heat and simmer until about half the cranberries have popped, about 5 minutes. Remove from the heat. Mix in the remaining ginger. Taste and add more sugar if desired. Transfer to a bowl and cool. (Can be prepared 3 days ahead. Cover and refrigerate.) Serve chilled or at room temperature.