Place the rhubarb, fresh ginger, granulated sugar, lemon juice, and 1 ¼ cups of water into a saucepan.
Heat the mixture over a medium-high heat, stirring occasionally. Allow the mixture to cook for around 5 minutes, until the sugar has completely dissolved and the rhubarb is falling apart. Set the pan aside to allow the mixture to cool.
Once cool, filter the rhubarb mixture through a muslin to remove the fruit pulp, and store the cooled rhubarb and ginger syrup in a sterilized bottle in the fridge.
To complete the cocktail, add a shot of the rhubarb and ginger syrup to a glass, along with a shot of gin. Muddle the ingredients together and then top with Prosecco.