Add all the ingredients to a saucepan and bring to a boil. Lower heat and let mixture simmer for 10 minutes. Remove from heat and allow to cool at room temperature. Strain into a clean container, seal and refrigerate.
Make the soda:
Combine water, syrup, cordial, lime and bitters in a tall measuring cup. Stir to combine and pour through a strainer into the whipping siphon.
Seal the container securely and add a Co2 charge. Be sure to tighten the charge cartridge until it pierces - you will hear the gas release. Tilt the whipper downward and shake firmly and vigorously three to five times.
Add ice to two glasses and squeeze the whipper lever firmly, while tilting it down into the glass. Garnish and enjoy!