Add mint leaves to a cocktail shaker and gently muddle to express their oils.
Add gin, fresh lemon juice, and simple syrup.
If using egg white, add it now and dry-shake (without ice) for 10 seconds to emulsify.
Add ice and shake vigorously for 12–15 seconds until well chilled.
Double-strain through a fine-mesh strainer into a chilled cocktail glass.
Garnish with a fresh mint sprig.
The South Side is said to have originated at the Chicago Athletic Association during Prohibition, where bootleg gin was softened with lemon and mint to mask its rough edges - making it one of the earliest examples of the modern gin sour.
My Bar Shelf reads your shelf and shows you every cocktail you can make from what you already own, including South Side.