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

Gradually whisk in milk until smooth, then place over medium heat.

Cook, stirring constantly, until the mixture thickens and begins to bubble, about 5-7 minutes.

In a small bowl, lightly beat the egg yolks. Slowly whisk in about 1/2 cup of the hot milk mixture to temper the eggs.

Pour the tempered egg mixture back into the saucepan and cook for another 2 minutes, stirring constantly.

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

Pour the pudding into serving dishes and cover with plastic wrap (directly on the surface) to prevent a skin from forming.

Chill in the refrigerator for at least 2 hours before serving.