Pour the egg yolks, sugar and cornstarch into a saucepan and whisk them together. Gradually beat in the cream and milk until smooth. Place the pan over medium heat, and stirring constantly, cook until the mixture thickens and comes to a boil. Switch off the heat, and stir in the vanilla extract. Transfer the custard to a bowl, cover the surface with plastic wrap to prevent a skin from forming, and leave out to cool.
Preheat the oven to 375 degrees F. Lightly grease a 12-count muffin pan.
Halve the puff pastry sheet horizontally. Set one half on top of the other, and set it aside for 5 minutes. Tightly roll up the puff pastry from short end to short end. Cut the puff pastry log into 12 (1/2-inch) rounds. Lay each piece on a lightly floured surface, and using a rolling pin, flatten out each round until they are 4-inches in diameter. Press each round into each muffin pan. Spoon the cooled custard into the pastry cases, and bake until the pastry and custards are golden, about 20 to 25 minutes. Leave the tarts in the pan for 5 minutes, and then remove and transfer to a wire rack to cool completely.