In a cocktail shaker, muddle the mint leaves and lime juice. Add the ginger simple syrup, pineapple puree, rum, and a couple ice cubes, and shake vigorously to combine. Pour into a cocktail glass filled with ice and top with a splash of club soda. Garnish with a fresh mint sprig and a couple lime slices if you’re feeling fancy.
For the Ginger Simple Syrup:
Place all the ingredients in a small saucepan and bring to a boil. Once the sugar has dissolved (it should only take about a minute), remove from the heat and let the mixture sit for 20 minutes. Strain into a jar (or other airtight container), cover and chill. The syrup will keep in the fridge for up to 2 weeks.
For the Pineapple Puree:
Place the pineapple in a blender and puree until smooth. (So simple!)