Place the bowl of an ice cream maker in the freezer for at least 24 hours, or according to manufacturer’s directions.
Place the California avocado and almond milk into a blender and puree until smooth.
Add the cocoa powder, maple syrup and vanilla extract. Blend until smooth, scraping down the sides of the blender as needed.
Transfer to a large measuring cup with a spout, cover and chill for 2 hours.
Pour the avocado mixture into the ice cream maker and process until the ice cream reaches the desired consistency. In the last 5 minutes, add the chopped dark chocolate.
If you would like the ice cream to be firmer, transfer to a freezer-friendly container and place in the freezer. Before serving, leave on the counter to defrost until easy to scoop.