Beat the eggs with the sugar and butter. Add the flour with baking powder and pour in the milk. You need to get a dough thicker than pancake dough.
Pour the mixture into an oiled tray, arrange the apricots, cut in 2, on top. Bake the cake in a moderately preheated oven.
When you take it out, sprinkle it with powdered sugar that you've mixed with the vanilla beforehand.