In a medium saucepan, whisk together the granulated sugar, cocoa powder, cornstarch, and salt.

Gradually whisk in the milk until the mixture is smooth.

Place the saucepan over medium heat, stirring constantly.

Keep stirring until the mixture comes to a gentle boil.

Once boiling, reduce heat to low and continue cooking for 2 more minutes.

Remove the saucepan from heat and stir in the vanilla extract and butter.

Transfer the filling to a mixing bowl and let it cool for about 10 minutes.

Once cooled slightly, pour the chocolate filling into your prepared pie crust.