Whisk 3 cups of milk, turbinado, and cocoa in a ceramic or anodized stainless steel saucepan over medium-high heat. Bring to simmer. Remove from heat.
Whisk 1 cup milk, arrowroot, salt, egg yolks, and vanilla in a medium to large bowl.
Temper the egg mixture by whisking while slowly adding the cocoa mixture.
Pour entire mixture back into the saucepan and whisk constantly over medium-high.
When it comes to a full boil you will notice the mixture thickening. Reduce the heat to simmer and continue whisking until thick (~3 minutes).
Split between 8 cups/bowls/ramekins. (Optional: cover with parchment paper or plastic wrap. I don't do this because I like the film that forms on top of the pudding. Try both and see which you like.)
Refrigerate for at least 6 hours.
Keeps in your refrigerator for up to 1 week.You can serve this pudding hot or cold!Alternate Serving: Blind bake a pie crust, fill with the pudding, and refrigerate for at least 6 hours for a chocolate pudding pie.