In a small saucepan, combine the brown sugar and water. Heat gently over medium heat, stirring just until the sugar fully dissolves. Do not boil. Remove from heat and let cool completely.
In a large bowl or pitcher, add the blackberries and mint leaves. Gently mash with a muddler or wooden spoon just until the berries release juice and the mint becomes aromatic. Do not purée — texture and clarity matter.
Add the fresh lime juice, verjus, and 80–100 ml of the cooled brown sugar syrup to the smash. Stir gently to combine. Taste — it should be bright, tart, lightly sweet, and vinous.
Add plenty of ice to the pitcher. Pour in the chilled club soda and add the pinch of fine sea salt. Stir gently once or twice only to integrate without killing carbonation.
Pour into ice-filled glasses and garnish with fresh mint sprigs, lime wedges, and blackberries.
