Pulse the blackberries and ¼ cup simple syrup in a blender. Pass the mixture through a chinois or fine mesh strainer.
Strip the leaves off a sprig of rosemary and muddle with 2 orange slices in a cocktail shaker. Add ice.
Add ⅓ cup of blackberry syrup and vodka to the cocktail shaker. Shake, pour into a Collins glass with ice. Top off with club soda and add a dash of orange bitters. Garnish with burnt orange peel strip and rosemary sprig.