Using a double old-fashioned glass with a single large ice cube, add the bourbon, Campari, and rosemary simple syrup. Stir well to combine and chill the cocktail. Garnish with a sprig of rosemary.
Peel and separate a satsuma and add the Campari. Gently mash the satsuma pieces to release some of the juice. Allow the satsumas and Campari to soak for at least 2 days.
In a small saucepan, combine the water and sugar and bring to a boil. Allow the mixture to boil for 5 minutes until starting to thicken. Remove from the heat and add the rosemary, allow the mixture to completely cool before using.