In a saucepan, bring the mint leaves, the sugar, and 3 cups of the water to a boil. Simmer for 5 minutes, stirring occasionally. Strain out mint leaves.
Meanwhile, in a bowl, sprinkle the gelatin evenly over 1/2 cup of the water and allow the gelatin to absorb the water for two minutes.
Stir in the boiling minty water and sugar mixture until gelatin is full dissolved. Stir in the bourbon.
In a blender blend the blackberries and about 2 cups of the gelatin mixture until it is liquefied. Pour through a wire mesh strainer back into the bowl with the remaining gelatin to strain out seeds. (My strainer is ridiculously small to go with my ridiculously small New York City kitchen. I suggest using a bigger strainer.)
Refrigerate the mixture until thickened to the consistency of a gel. Stir to evenly disperse the pureed fruit throughout and spoon into a 5-cup mold or several individual molds. Refrigerate until firm, about 8 hours or overnight.
To unmold, fill a sink, basin, or large bowl with warm water. Dip the mold just to the rim in the warm water for about 15 seconds. Lift from water, hold upright, and shake slightly to loosen the gelatin from mold. Place a cold, moistened plate over the top of the mold and invert the plate and mold together. Carefully lift the mold, if gelatin does not release dip the mold in the warm water and try again. Garnish with a mint sprig and serve.