In a saucepan, combine the milk, granulated sugar, and vanilla extract, and warm gently over medium heat until the sugar dissolves and the mixture becomes hot, but not boiling.

Separately, whisk together the egg yolks and cornstarch in a small mixing bowl until a uniform paste forms.

Remove the heated milk from the burner and carefully ladle a few tablespoons into the egg mixture while whisking vigorously to temper the yolks. Gradually add more of the warm milk, continuing to stir, until approximately half the liquid has been mixed in.

Return the saucepan to the heat and slowly pour in the tempered egg mixture, whisking continuously.

Maintain medium heat and stir constantly until the custard thickens and reaches a soft boil, achieving a rich, pudding-like texture.

Transfer the thickened custard into individual serving dishes. Serve immediately while warm or cover with plastic wrap and refrigerate to enjoy chilled.