In a saucepan, combine sugar, cocoa powder, salt, and cornstarch. Mix well. Add in cold milk, whisk until combined.
Increase heat to medium, stirring constantly until mixture reaches a boil*.
As soon as the pudding has thickened, remove from the heat and stir in butter and vanilla.
Allow mixture to cool completely, stirring occasionally to avoid a skin forming on the pudding.
Serve chilled or warm.