Add cider, brown sugar, cinnamon stick, and salt in a medium saucepan and stir to combine.
Bring to a boil and then lower heat to a simmer.
Let mixture simmer for 20-30 minutes, until it reduces by about half and has thickened (syrup will continue to thicken as it cools).
Remove cinnamon stick and pour syrup into a jar or other airtight container and place in fridge to cool completely.
Syrup should keep fresh for about 1 month when stored properly.