In a saucepan, pour 3 cups (720 ml) of whole milk and bring it to a gentle simmer over medium heat.
While the milk is heating, in a separate bowl, mix the remaining 1 cup (240 ml) of milk with the cornstarch until smooth.
Once the milk in the saucepan is simmering, gradually whisk in the sugar until dissolved.
Slowly pour the milk and cornstarch mixture into the saucepan, whisking constantly to prevent lumps from forming.
Continue cooking and stirring the mixture over medium heat until it thickens to a pudding-like consistency, which should take about 10-12 minutes.
Once thickened, remove the saucepan from heat and stir in the vanilla extract.
Pour the pudding into individual serving dishes or a large bowl.
Let the pudding cool for a few minutes at room temperature, then cover it with plastic wrap, making sure the plastic wrap touches the surface of the pudding to prevent a skin from forming.
Chill the pudding in the refrigerator for at least 2 hours, or until completely set and chilled.
Serve the milk pudding cold, optionally garnishing with fresh fruit or whipped cream, if desired. Enjoy!