Put the milk into the saucepan and bring it to a boil with the vanilla.

If you are using a vanilla bean, you have to split the bean open lengthwise with a knife and scrape the insides to get out all the little black seeds. Add these to the milk, along with the bean itself.
 

In a mixing bowl, mix together the sugar with the whole eggs and the egg yolks, using your whisk.

Slowly pour the hot milk into this mixture while stirring it.
 

Cut the apricots in half and take out the stones. Put the apricots into a buttered baking dish and sprinkle them with sugar. Put the baking dish into the oven for 15 minutes. Let the apricots cool off for 15 minutes outside the oven.

Then place the apricots into the other baking dish and pour the egg and milk mixture over top, leaving part of the apricots showing.
 

Cook the custard in a water bath in the oven at 180° C (350° F) for 35 to 40 minutes. After you take the custard out of the oven, let it cool (but don't put it in the refrigerator). Serve slightly warm, or cold, depending on your taste.

You can also make the custard in four deep plates. Divide the apricots and the custard mixture among the plates. Cook in the water bath in the oven, but only for 30 minutes.

The appearance of this dessert will make you think of fried eggs!