Start by boiling your 2 cups of water with the 2 cups of sugar until fully dissolved. Remove from the heat and stir in your lime zest with the 1/2 cup mint leaves. Cool to room temperature, strain, and refrigerate.
Drop your lime wedges into the bottom of a large pitcher. Stir in your remaining mint leaves, 1 cup of your premade syrup, rum, and lime juice. Top with your club soda and enjoy!