In a medium bowl, combine sugar, cocoa, cornstarch, and salt and mix to combine.
Whisk in cold milk until combined.
Pour this mixture into a medium saucepan over medium heat, and while whisking constantly, cook until mixture reaches a boil. Let boil for 1 minute, still stirring.
After 1 minute, remove from heat and whisk in butter and vanilla.
Let cool for 20 minutes, then place plastic wrap directly onto the surface of the pudding, to prevent a skin from forming and chill until ready to serve.
This simple creamy chocolate pudding recipe is easy to make at home for a deliciously decadent dessert you can't help but love!