Combine raspberries, white rum, lime juice and raspberry balsamic syrup in the glass part of a shaker. Add ice and long shake (shake for a long time). Give it a taste, add simple syrup for balance if necessary.

Strain into a rocks glass with crushed ice. Garnish with a lime wedge.

For the Raspberry Balsamic Syrup:

Place the raspberries and balsamic vinegar in a bowl to soak. In a pot, over medium heat, combine the sugar and water. Stir until the sugar dissolves. Add the raspberry and vinegar mixture to the pot, bring to a boil and then reduce heat and let simmer for 35 minutes, stirring periodically. Remove from heat, strain and store in the fridge for up to a month. 

Cheers!