For the Cinnamon Syrup
Combine the sugar, water, and cinnamon stick in a medium saucepan over medium-high heat. Bring the mixture to a rapid boil, stirring to dissolve the sugar. Remove from the heat and let cool. Strain the syrup and store in an airtight container in the refrigerator for up to 1 week.
To make the drink
Fill an Old Fashioned glass with ice. Pour in the bourbon and cinnamon syrup. Stir gently to combine. In a separate Old Fashioned glass, add a few drops of amaretto and turn the glass to coat it in the liqueur. Pour out the excess amaretto. Strain the bourbon mixture into the amaretto glass. Add one or two cubes of ice, if desired.