Put water, ginger and peppermint leaves in a saucepan. Bring to a boil then cover the saucepan with a lid for 5 minutes and simmer over gentle, low heat.
Turn off the heat and remove the lid and add in the tea bags. Allow it to infuse for 510 minutes, covered.
Remove the cover and add in the sugar. Stir until sugar dissolves and leave the ginger syrup aside to cool completely.
Sieve and pour the cooled ginger concoction into a punch bowl. Add in the ginger ale or beer, if preferred. Add in plenty of ice cubes, put some freshly-sliced lemon pieces and a few fresh peppermint leaves as garnishing, and throw in 56 maraschino cherries too.