In a medium-sized saucepan, whisk together the granulated sugar, brown sugar, cocoa powder, salt, and cornstarch until well-blended and smooth.

Add the egg yolks to the dry mixture along with about 1/3 cup of whole milk. Whisk vigorously until smooth.

Place the saucepan over medium heat and gradually whisk in the remaining milk. Stir continuously for about 5 to 10 minutes until it thickens.

Once thickened and bubbly, carefully remove from heat and stir in the unsalted butter and vanilla extract until fully melted.

Pour the pudding into a suitable container, cover with plastic wrap directly on the surface, and chill in the refrigerator for at least 4 hours.