In a small, heavy-bottomed saucepan, combine sugar, cinnamon stick and water; bring the mixture to a boil, stirring often.
Cook, stirring occasionally, until the mixture is a deep, caramel color and has the consistency of a thin syrup (about 10-15 minutes).
Remove from heat and stir in the cream; return saucepan to high heat and boil the mixture until it is the consistency of a thick syrup (about 2 minutes).
Stir in the coffee; cool syrup.
Strain the coffee syrup through a fine strainer into a heatproof jug. (I completely skipped this step. I didn't have a fine enough strainer and it tasted amazing without straining.)
The syrup should be refrigerated until ready to use (allow it to reach room temperature before drizzling over the cupcakes).