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

Gradually stir in the whole milk into the dry mixture while whisking continuously.

Place the saucepan over medium heat and cook, stirring constantly, until the mixture reaches a full boil and thickens, about 5-7 minutes.

Remove from heat and stir in the unsalted butter and vanilla extract until fully combined.

Pour the pudding into serving dishes and let it cool at room temperature before refrigerating for at least 2 hours to set.