Begin by slapping the fresh tarragon to bring out the aromatics. Drop the tarragon into a cocktail shaker, reserving a few leaves for the garnish. Add the lime juice, vodka, and honey syrup to the shaker. Add 2 ice cubes to the shaker, and short shake to make the liquid cold without diluting it. Strain the mixture into a high ball glass filled with 4 more ice cubes. Top the glass with the soda water, and use the reserved tarragon for the garnish.
*3 parts honey, 1 part water