Whisk Dry Ingredients.In a medium saucepan, combine coconut sugar, cornstarch, cocoa powder, and salt. whisk to combine until well blended.
Add Milk & Cook. Next, pour in coconut milk and almond milk, then whisk and cook over medium heat 8-10 minutes, or until the mixture comes to a low simmer and pudding has thickened. (You should be able to see the path of the whisk in the pudding and if you let pudding drip off the whisk back into the saucepan, it should rest on the surface of the pudding briefly before absorbing.
Add Chocolate & Vanilla. When the pudding has thickened, turn off the heat and mix in chocolate chips and vanilla extract. Whisk until the chocolate has full melted and the pudding is smooth. (You will likely see some bubbles, but there shouldn't be any lumps. If, by chance you do have lumps, you can strain the pudding through a fine mesh sieve before refrigerating.)
Cover & Chill. Pour the chocolate pudding into a heat-proof bowl and press plastic wrap onto the surface to prevent the pudding from developing a "skin" on top of the pudding. Transfer to the refrigerator and chill at least 3-4 hours to thicken completely. If you check it after 1-2 hours, it'll still be on the thin side.
Serve & Store. Spoon the pudding into individual dishes and top with whipped coconut cream, fresh berries, chocolate, etc. as desired. Leftover pudding will keep in an airtight container the refrigerator 3-4 days.