For the mint simple syrup, add the sugar, water and mint sprigs to a small saucepan. Bring to a boil and reduce to a simmer, stirring occasionally. Once the sugar dissolves, turn off the heat and allow the mint sprigs to steep for about 10 minutes. Remove the mint sprigs.

Cut off the end pieces of the cucumbers and peel. Roughly slice into small chunks. Add a small amount of cucumber chunks to a blender with a splash of water and puree until smooth. Continue adding a few cucumber chunks at a time and puree until all the cucumber has been processed.

In the sink, place a bowl or measuring cup under a fine-mesh sieve. Pour the cucumber puree into the fine-mesh sieve and allow to drain until you have 1 ½ cups. Although you can use a cheesecloth in the fine-mesh sieve for extra straining, it's not necessary. If you have more than 1 ½ cups of cucumber juice, you can freeze it for another time.