Make the vanilla sugar: Grind the sugar and vanilla seeds in a blender until powdery (like confectioners' sugar). Store in an airtight container for up to 1 month.
Make the drink: Fill a tall glass with ice to chill it. Muddle the strawberries, 2 teaspoons vanilla sugar and 3 tarragon sprigs in a cocktail shaker. Add the bourbon and Pernod. Add ice, then cover and shake well. Dump the ice out of the glass. Refill with crushed ice, then strain the drink into the glass. Crush the remaining tarragon sprig with the flat side of a knife; add to the drink.