Pour the milk, cream and vanilla into a saucepan, and bring it just to the boil over medium-high heat.
Once the mixture starts to bubble, immediately take the pan off the heat.
In a large mixing bowl, whisk together the eggs, egg yolks, sugar and cornflour (US: cornstarch).
Add a few splashes of the hot milk mixture into the eggs, quickly whisking as you do so. Then gradually whisk in the remaining milk mixture in a slow and steady stream.
Pour the custard through a fine strainer into a large jug. The strainer will remove any pieces of cooked egg in the mixture, so that you will have a silky smooth custard.
Set the jug aside for about 5 minutes to cool slightly.
If, at this stage, the caramel in the jars have not set (i.e. you can see the caramel move as you swirl the jars), it probably means that your caramel was too thin (maybe you added too much water) or your room is very warm. Simply place the jars in the fridge for about 5 minutes for the caramel to set completely. See my Kitchen Tips below.
Place the glass jars into a high-sided baking pan or an oven-proof saucepan. Pour the custard mixture into each glass jar.