In a medium saucepan over medium-low heat, combine the heavy cream, half & half, and coconut cream. Stir occasionally and avoid scalding. Cook until just before a low simmer. Remove from the heat.
In a large bowl, beat the egg yolks and sugar with a hand mixer or whisk until well incorporated and lightened in color.
Temper the egg and sugar mix by slowly adding the hot cream mixture one ladle-full at a time, and mixing with each addition until 1/3 of the cream mix is in the bowl. You want to add the cream gradually or you will be making scrambled eggs in the bowl!
Add the rest of the cream mix and whisk. Return to the pot. The ice cream base should be about 170F-175F at this point (it could coat the back of a spoon), if the temperature is too cool, heat gently while stirring continuously.
Once at temperature, remove from the heat and return to the large bowl. Allow to cool to room temperature and stir in the vanilla extract. Cover with plastic wrap and chill for at least 4-6 hours.
Before churning your ice cream, take the shredded coconut and chocolate chunks and place into a medium mixing bowl. Place in the freezer to chill.
After the cream base has chilled, place the ice cream mix into the bowl of your ice cream maker and follow the manufacturer's directions for churning. I churned for 25 minutes before adding in the cold chocolate and shredded coconut.
Churn an additional 5-7 more minutes, and then pour into an airtight container. Place a layer of plastic wrap directly on top of the ice cream and then seal the lid.
Turn you freezer up a few degrees and chill overnight. This is a very rich custard, so it needs a lower temperature to set.