In a medium saucepan, whisk together the granulated sugar and cornstarch until well combined. This prevents lumps.
Gradually whisk in the evaporated milk and sweetened condensed milk until smooth.
Place the saucepan over medium heat. Cook, stirring constantly with a whisk or wooden spoon, until the mixture thickens and begins to bubble. This should take about 8-10 minutes. Do not boil vigorously.
Once thickened, remove the saucepan from the heat. Stir in the vanilla extract and a pinch of salt.
Pour the pudding mixture into individual serving dishes or a larger bowl. Cover the surface directly with plastic wrap to prevent a skin from forming.
Chill in the refrigerator for at least 4 hours, or until firm and well-chilled. The longer it chills, the firmer it will become.
Before serving, remove the plastic wrap. Garnish with fresh fruit, a dollop of whipped cream, or chocolate shavings as desired.