In a medium pot, combine the sugar, cocoa powder, and 2 cups of whole milk. Stir frequently over medium heat until it becomes steamy but not boiling.

In a separate bowl, whisk together the egg yolks, cornstarch, and remaining quarter cup of whole milk until smooth.

Remove the pot from the heat and temper the egg mixture by slowly whisking in about a cup of the hot cocoa mixture.

Whisk in the remaining hot cocoa mixture and return the pot to the heat.

Cook the mixture over medium heat, whisking constantly until it reaches the desired consistency. The pudding will thicken suddenly, and you’ll see trails being dragged through by the whisk.

Remove the pot from the heat and whisk in the cubed butter and vanilla extract until melted and combined.

Transfer the pudding to a clean bowl and cover with plastic or parchment paper to prevent a skin from forming. Chill until set.

Serve in cups topped with whipped cream and shaved chocolate, if desired.