In a heavy saucepan, whisk together the sugar, cocoa powder, cornstarch, and a pinch of salt. Break up any lumps thoroughly — lumps of cornstarch or cocoa now will survive into the finished pudding.

Add the milk gradually while whisking, stirring until the mixture is completely smooth with no streaks or lumps. Starting with the dry mix before adding liquid is what keeps it lump-free.

Place over medium heat and whisk constantly. Make sure to reach the edges of the pan with every stroke — that’s where scorching starts. After 6–8 minutes the pudding will thicken noticeably and come to a gentle boil. Let it boil gently for 1 full minute to cook out the cornstarch.

Remove from heat. Add the chopped chocolate and stir until fully melted and smooth. Add the vanilla extract and butter, stirring until the butter is completely incorporated and the pudding is glossy.

Pour into a bowl or individual ramekins. Press a sheet of plastic wrap directly onto the surface of the pudding (to prevent a skin from forming — unless you’re into that). Cool to room temperature, then refrigerate for at least 2 hours. The pudding will seem loose right after cooking; it thickens significantly as it chills.