For the apple cider syrup: In a small saucepan over medium heat, combine sugar and water. Bring to a simmer and stir to dissolve the sugar. Turn off heat and set syrup aside.
Heat a grill to high heat. Core and cut the apples into 1/2-inch-thick slices on the equator (leave skin on). Grill apples 4 for 5 minutes on each side. Place apples in a high-speed blender with the syrup. Blend until smooth. Strain and set aside. (Apple cider syrup will last in the refrigerator for up to 14 days).
For the cocktail: Fill a large pitcher with ice. Add the bourbon, lemon juice and 9 ounces of the apple cider syrup. Stir and pour into tall Collins glasses filled with ice. Garnish each drink with a sage leaf.
The syrup can be smoked using a kitchen smoker over hickory wood. Follow smoker directions.