Add all ingredients to a small saucepan and set over medium heat. Cook, stirring occasionally, until heated through and the sugar has dissolved, about 5 minutes. Remove from heat and let sit for 15 minutes. Remove cinnamon stick. Keeps refrigerated in an airtight container for up to 1 week.
For the iced coffee:
Fill a tall glass with ice cubes. Add coffee concentrate, 2 tablespoons of cinnamon dolce syrup (add less or more depending on your preference), and half and half to desired point of creaminess. Drop in a straw and serve.