Place a sauce pot over medium heat. Add the half-and-half, cream, egg yolks, 3/4 cup sugar and salt. Whisk well. Continue to whisk as the mixture warms and thickens. Bring to a low boil, then remove from heat.
Stir in the vanilla and anise extracts. Place the lid on the pot and refrigerate for at least four hours or overnight. *If you're in a hurry, place in the freezer for 1 hour, but stir every twenty minutes. Don't forget about it!
Chop the blackberries into small pieces. Toss with 2 tablespoons sugar. Turn on the ice cream machine. Place a sieve over the top to remove any egg clumps, and pour the ice cream mixture into the frozen ice cream bowl.
Churn for 20+ minutes until thick, like soft serve ice cream, then add the blackberries and juices. Churn another minutes or so, then scoop into an airtight container and freeze.