In a small saucepan, combine the brown sugar and water. Heat gently over medium heat, stirring just until the sugar fully dissolves. Remove from heat and add the lemon peel strips. Let steep for 5 minutes, then remove and discard the peel. Let the syrup cool completely.
Scoop the lemon pulp into a bowl, removing all seeds. Smash thoroughly with a spoon until the fibers loosen and juice is released. Do not strain — texture is the point.
Add the basil leaves and a pinch of fine sea salt to the lemon pulp. Gently smash just a few times until aromatic. Stop early. Over-muddling turns basil bitter and swampy.
Add 80–100 ml of the cooled lemon peel syrup to the mixture. Stir gently and taste. The base should be sharp, herbal, and lightly sweet — never syrupy.
Add plenty of ice to the pitcher. Pour in the chilled club soda last and stir gently once or twice to integrate without killing carbonation.
Pour into ice-filled glasses and garnish with fresh basil leaves and lemon peel twists.