Whisk together the cream, cocoa, and sugar in a saucepan. Heat it until it comes to a boil, whisking frequently.

Once it boils, remove from heat and add in vanilla and blackberries. Stir to mix.

Cover and let stand for 10 minutes.

Puree the mixture with an immersion (or regular) blender.

Chill the mixture in the freezer for approximately 20 minutes, then freeze in your ice cream maker according to manufacturer’s directions.

Once the mixture has started to thicken into ice cream, add the shaved chocolate bits a spoonful at a time so that they incorporate into the mixture without clumping.