Put the brown sugar in a blender and turn it into powdered sugar with a few turns. Cut the ginger and lemon (complete with peel) into large cubes and add both to the sugar in the blender. Puree until a thick paste is formed. Then add the still water and mix again vigorously. Then fill into a bottle through a fine sieve. Put in a cool place.
Pour the chilled lemonade into a glass and top up with carbonated mineral water as desired. Possibly add a few more ice cubes and lemon wedges.