Serving suggestions: Serve on toasted bread, alongside cheeses, or on lamb chops. Mix with yogurt and granola, or layer in desserts or parfaits.
Place the blackberries and their juice in a medium saucepan and lightly mash with a fork. In a food processor, combine the basil, sugar, orange juice and lemon juice. Blend until smooth. Stir the mixture into the blackberries and bring to a simmer over medium heat. Simmer until the mixture is thick, stirring occasionally, 25 to 30 minutes. Remove the pan from the heat and allow the jam to cool for 1 hour (the jam will continue to thicken as it cools). Refrigerate in an airtight container for up to 3 days.