In the base of a cocktail shaker, muddle three cucumber coins with the Lemon Simple Syrup. Add the Pimm’s No. 1 and two ice cubes, and shake for at least 30 seconds, until the shaker is frosty. Line the inside of a tall glass with the length of cucumber garnish, pile high with ice, and pour in the contents of the shaker. Top the glass with the ginger beer and serve with a candied lemon peel left over from making your simple syrup if you like.
Remove the zest from the lemon with a vegetable peeler in long strips, leaving the white pith behind. Juice the lemon into a small bowl.
Combine the sugar and water in a small saucepan over medium-high heat, stirring until the sugar dissolves. When the mixture starts to simmer, add the lemons peels and lemon juice to the pan, and reduce the heat to low. Simmer for 30 minutes, uncovered, until the syrup has reduced and thickened slightly.
Remove saucepan from heat and allow to cool. Transfer the syrup to an airtight jar or bottle, reserving the now-candied lemon peels with the syrup for later use as a garnish.
To Prepare the Cucumber: Cut the ends off of your cucumber and discard. From one end, slice off three coins about ¼ inch thick per drink. These slices will be muddled into the drink. To make the garnish, use a mandolin or y-shaped vegetable peeler to slice the cucumber along its length, creating a long and very thin cucumber slice to line the inside of the glass. Reserve remaining cucumber for future drinks or another use.