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

Gradually add the milk while whisking to combine.

Cook over medium heat, stirring constantly until the mixture thickens and starts to bubble.

Remove from heat and stir in the butter and vanilla extract until smooth.

Pour the pudding into serving bowls and cover with plastic wrap to prevent a skin from forming.

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