In a small saucepan, add organic cane sugar and water. Bring to a boil and then turn heat to low, stirring often until sugar has dissolved. Remove from heat and add mint. Allow to steep for about 15 minutes, then strain simple syrup into an airtight jar or container. Store in the refrigerator.
Add ice to a cocktail shaker followed by the gin, mint simple syrup, and lime juice. Shake then strain into a chilled cocktail glass or Old Fashioned glass. Garnish with mint.