In a heavy-duty saucepan, combine all the syrup ingredients. Bring the water to a slight boil, letting the sugar dissolve, then turn the heat down to medium-low. Let the syrup go for about 30 minutes.

Remove from heat and let cool slightly, then strain the syrup into a jar or squeeze bottle you can cover. Keep the now-crystallized ginger for your drinks or as a snack. Chill the syrup until ready to use; it keeps refrigerated for 2 to 3 weeks.

Combine the mint, lime wedges, and ginger syrup in a tall glass. With a muddler or the end of a wooden spoon, crush them together until you smell the aroma of the mint and it is well broken down.

Add a little ice, then the bourbon, and stir together. Add a little more ice, top with soda water, and stir slightly. Garnish with mint and crystallized ginger.