Place both coconut milk and coconut cream in a saucepan and heat until they are melted but not boiling.
Turn off the heat and add peppermint flavor.
Pour mixture into a glass container and place in the fridge for several hours until very cold.
Pour mixture into your ice cream maker and process per manufacturer's instructions.
While your ice cream is in the ice cream machine, place the bowl back in the refrigerator to stay *cold. This helps when you pour your ice cream into the bowl. It allows you to add chocolate chips, stir and combine without the ice cream melting as fast.
When done, pour ice cream into your cold bowl, add chocolate chips and chopped chocolate and stir to combine.
Either consume immediately or place in the freezer until more frozen and then scoop ice cream and serve.
Notes: Placing an empty bowl back in the fridge while ice cream is being made in ice cream maker is helpful because this will give you time to add chocolate chips/chocolate chunks and stir before it all starts melting.
If you freeze prepared ice cream for longer than several hours, it will become very hard. You will simply need to remove from the freezer, place a room temperature for a period of time (20 minutes?) until it is soft enough to scoop. Some preparation in advance is necessary, but so worth it!