In a medium bowl, whisk together the egg yolks, sugar, cornstarch, and salt until well combined and slightly lighter in color.

In a medium saucepan, heat the milk over medium heat until steam begins to rise from the surface and small bubbles form around the edges. Do not allow it to come to a full boil.

Carefully ladle about 1 cup of the hot milk into the egg mixture, whisking constantly to prevent the eggs from cooking. This process is called tempering.

Gradually pour the tempered egg mixture back into the saucepan with the remaining milk, whisking continuously.

Return the saucepan to medium-low heat and cook, stirring constantly with a wooden spoon or heat-resistant spatula, until the custard thickens enough to coat the back of the spoon, about 5-7 minutes.

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

For an extra-smooth texture, strain the custard through a fine-mesh sieve into a clean bowl.

To serve warm, portion into dessert dishes immediately. For chilled custard, press a piece of plastic wrap directly onto the surface to prevent a skin from forming and refrigerate for at least 2 hours.