Set out two small plates. On one plate, add the sugar. On the second plate, add the lime juice. Twirl the rim of three lowball glasses first through the lime juice and then the sugar.
Carefully fill each glass with crushed ice.
In a cocktail shaker, add blackberries, lime juice, and granulated sugar. Muddle the mixture until the blackberries release their juices.
Add bourbon and ice to the shaker. Cover and shake until well chilled.
Strain the blackberry mixture evenly over the ice in the glasses.
Top each glass with ginger beer and garnish with blackberries.