In a medium saucepan, whisk together one cup of milk, sugar (adding what you like for your sweetness level), salt, and cocoa powder.
Bring the mixture to a simmer over medium-high heat.
Remove from the heat.
Meanwhile, whisk the remaining 1/2 cup of milk, egg yolks, tapioca starch, and vanilla in a bowl.
Gradually whisk the hot milk into the egg mixture.
Return mixture to the saucepan and cook over medium-high heat, whisking constantly, until the pudding comes to a boil.
Reduce the heat a bit, but maintain a simmer, and continue whisking until thick, about two more minutes.
Remove from heat and pour into cooled pie crust.