1. Place all the ingredients, except for 1 cup of the blackberries, in a blender and process until smooth.
2. Strain through a fine mesh strainer to remove the seeds.
3. Chill the mixture (or begin with chilled ingredients) if required by your ice cream machine, pour the mixture into the ice cream machine, and freeze it according to the manufacturer's instructions.
4. Serve topped with the remaining berries.