Bring first 4 ingredients to a boil in a saucepan, stirring constantly; reduce heat, and simmer 15 minutes. Cool.
Process blackberry mixture, in batches, in a blender or food processor until smooth, stopping to scrape down sides.
Pour blackberry puree through a fine wire-mesh strainer into a bowl, pressing pulp with back of a wooden spoon. Discard pulp, and stir in buttermilk. Freeze 8 hours.
Process frozen blackberry mixture, in batches, until smooth. Freeze 5 hours.
*5 (14-ounce) packages frozen blackberries, thawed , may be substituted.
Note: Recipe may be halved.