In a cocktail shaker, add the mint leaves and lime juice and gently muddle to release the mint's flavor.
Pour in the simple syrup and gin.
Fill the cocktail shaker with ice, secure the lid, and shake vigorously until the mixture is well chilled, about 15 seconds.
Fill a highball glass with ice and strain the chilled gin mixture into the glass.
Top off the glass with soda water to your taste, gently stir to combine.
Garnish with a sprig of fresh mint and a lime wedge for a touch of color and extra aroma.