In a medium-saucepot add the milk, sugar, and vanilla extract.
In a small bowl combine the egg yolks and cornstarch and mix together with a fork or whisk until it becomes a smooth paste.
Heat the milk up, medium heat, until it gets hot and the sugar dissolves. Don't let it get too hot, not scalding or boiling, just really warm.
Take the pot off the stovetop and pour a few tablespoons of it into the bowl of egg yolks. Stir the egg yolks really quickly, this will help prevent them from cooking. Then pour in a little bit more and keep stirring, etc. until half of the sugar milk has been incorporated. Replace the pot back on the stovetop.
Pour in the egg/milk mixture into the pot and stir until it is all combined. Keep heating and stirring until it thickens up and comes to a rolling boil. This process will cook the eggs and give a nice thick pudding type consistency.
Pour into small bowls and serve warm or cover them with plastic wrap and chill in the fridge for later. Enjoy!