Muddle the cucumber and mint in the bottom of a cocktail shaker until the cucumbers is smashed and the mint is broken down into small pieces. Add limes and continue muddling until the limes release their juices.
Add enough ice to fill your shaker two thirds of the way to the top. Add gin and agave. Put the perforated lid and the cap on the shaker and shake really hard for a good minute. Condensation will form on the outside of the shaker and it will be very cold to the touch.
Remove the lid and pour the cocktail through the perforated cap into a martini glass and garnish with a cucumber wheel and a sprig of mint. If you have muddled correctly there will be a few small pieces of mint happily swirling around in your drink.