To make the syrup, add all ingredients to a small saucepan and heat over medium-high while stirring often. Once the sugar has dissolved and the mixture is simmering, remove from heat, cover and allow to infuse for 30 minutes. Cool completely to room temperature, and strain through a fine mesh sieve before using. Note: For easy cocktail-making, my favourite way to store this syrup is in a squeeze bottle with a cap.
To make the cocktail, fill a cocktail shaker with ice and add jalapeno syrup, vodka and lime juice. Shake together and strain into a coupe glass. Garnish with a fresh jalapeno slice to serve.