Preheat the oven to 325°F (163°C).
In a medium saucepan, heat the whole milk over medium heat until it just begins to simmer. Remove from heat.
In a medium bowl, whisk together the granulated sugar, egg yolks, cornstarch, and salt until smooth and pale.
Gradually pour about half of the hot milk into the egg mixture, whisking constantly to temper the eggs.
Pour the tempered egg mixture back into the saucepan with the remaining milk, whisking continuously.
Return the saucepan to medium heat and cook, stirring constantly, until the custard thickens and coats the back of a spoon, about 5 to 7 minutes. Do not let it boil.
Remove the saucepan from heat and stir in the vanilla extract and unsalted butter until fully incorporated.
Divide the custard evenly among 4 heatproof custard cups or ramekins.
Place the custard cups in a baking dish and pour hot water into the dish until it reaches halfway up the sides of the cups.
Bake in the preheated oven for 30 to 35 minutes, or until the custards are set but still slightly jiggly in the center.
Carefully remove the custard cups from the water bath and let them cool to room temperature.
Refrigerate the custard cups for at least 2 hours before serving to allow them to fully set and chill.