1. Process blackberries in a blender until smooth. Pour through a wire-mesh strainer into a 1-qt. jar with a tight-fitting lid, discarding solids.
2. Add pisco and next 3 ingredients to jar. Cover with lid, and shake vigorously 30 seconds or until foamy. Pour mixture into 4 (10-oz.) glasses filled with ice. Top each with a dash of bitters, if desired. Serve immediately.