In a medium saucepan, whisk together the sugar, cornstarch, and salt.

Gradually whisk in the milk until smooth. Place the saucepan over medium heat and cook, stirring constantly, until the mixture thickens and comes to a gentle boil, about 5 minutes.

Place the egg yolks in a small bowl. Slowly pour about 1/2 cup of the hot milk mixture into the egg yolks while whisking constantly to temper them.

Pour the tempered egg yolk mixture back into the saucepan. Cook over medium heat, stirring constantly, for 1-2 more minutes until very thick.

Remove the saucepan from the heat. Stir in the peanut butter, butter, and vanilla extract until completely smooth and combined.

Pour the pudding into 6 individual serving cups or a large bowl. Press plastic wrap directly onto the surface of the pudding to prevent a skin from forming.

Refrigerate for at least 2 hours or until fully chilled and set. Serve topped with whipped cream and crushed peanuts if desired.