In a medium saucepan combine the sake and mirin and carefully flambe. When the flames die out, add the water and 1/2 cup sugar. Stir until the sugar dissolves. Stir in the miso and, using an immersion blender, dissolve the miso into the liquid. Transfer the mixture to a double boiler and cook until caramel in color and all of the lumps are gone, abut 45 minutes. Cool.