In a small bowl, mash together the blackberries, sugar and vanilla and let sit at room temperature until juicy, about 20 minutes. Strain the mixture through a sieve into a bowl, pressing against the solids with a rubber spatula; discard the seeds.
For each drink, place about 3 tablespoons of the blackberry syrup and 8 mint leaves into a cocktail glass and muddle together using the handle of a wooden spoon. Fill with crushed ice, 1/4 cup bourbon and a splash of seltzer. Garnish with a mint sprig.