In a small saucepan, combine the sugar and water. Heat gently over medium heat, stirring just until the sugar fully dissolves. Do not boil.
Remove from heat and add the rosemary sprig and the pinch of fine sea salt. Let steep for 5–6 minutes, just until lightly aromatic. Remove and discard the rosemary. Let the syrup cool completely.
In a pitcher, combine the fresh blood orange juice and 60–80 ml of the cooled rosemary syrup. Stir gently and taste. The base should be juicy and lightly sweet, not syrupy.
Add plenty of ice to the pitcher. Pour in the chilled club soda and stir gently once or twice to integrate without killing carbonation.
Pour into ice-filled glasses and garnish with blood orange slices and twists of blood orange peel.