In a medium-sized pot, whisk together whole milk, granulated sugar, and cornstarch over medium heat. Stir until thicken and bubbles form, about 5-7 minutes.

In a separate bowl, gently beat the egg yolks and slowly add about ½ cup of the hot milk mixture, whisking continuously.

Return the tempered yolk mixture to the pot with the remaining milk mixture. Cook over medium heat for about 1 additional minute, stirring constantly.

Remove from heat and stir in the vanilla extract and salted butter until fully incorporated.

Pour pudding into serving bowls, cover with plastic wrap, and let cool for about 15 minutes before refrigerating. Chill for at least 2 hours.