Add all of the ingredients to a small saucepan and bring to a boil over medium-high heat. Stir to ensure that the sugar is dissolved then reduce the heat to low and let the liquid simmer on low until the syrup forms. This should take about 20-25 minutes. Remove from the heat and let the syrup cool.
The Old Fashioned
Add the spiced apple syrup, bitters, and bourbon to a mixing glass and stir together. Add in the ice and stir until the glass is chilled and the cocktail has reached your desired dilution.
Add one large ice cube to an old-fashioned glass and pour the cocktail over the ice. Garnish with smoked rosemary and enjoy!