1. Place half of a lemon and the blackberries into a cocktail shaker and lightly press with the back of a bar spoon.
2. Add remaining ingredients, including one sage leaf, to cocktail shaker with ice and shake vigorously.
3. Strain into a rocks glass over ice.
4. Garnish with remaining two sage leaves and a sprig of thyme.
*Demerara Syrup can be purchased, or homemade by combining a 1:1 ratio of Demerara sugar and water in a saucepan over medium heat until sugar dissolves.