Optionally peel the ginger using a spoon to remove the skin.
Crush mint in a small bowl with a small mortar and pestle (I used a wooden lemon juicer), and set aside.
Chop the ginger into chunks, small enough to blend easily in a blender or food processor.
Bring 5 cups of water to a boil in a kettle or pot.
While the water is heating, puree the ginger with one cup of water in a blender or food processor until the ginger is thick and pasty.
Remove the pot of water from the heat, add the ginger paste and mint, and stir well.
Strain the mixture through a cheesecloth over a large glass pitcher, then squeeze the juice from the ginger paste into the pitcher. Discard the remaining pulp.
Stir in the lemon juice and sugar until the sugar dissolves, and serve garnished with mint leaves.
Serve it over ice or hot in a mug.