Stir together the gin, lemon juice, and honey syrup in a cocktail shaker, making sure the honey dissolves completely. Slap 1 rosemary sprig between both of your hands or gently pinch it all over to release the oils and add to the shaker. Fill the shaker with ice, cap and shake vigorously until the cocktail is well chilled. Using a Hawthorne strainer, double strain through a wire mesh sieve into an ice filled highball glass. Top with club soda and stir gently. Garnish with remaining rosemary sprig.