Strain all the liquid off the apricots. Separate the eggs, putting the yolks and whites in separate bowls. Whisk the yolks and oil together.
Combine the dry ingredients and gradually stir them into the yolk mixture, alternating with the milk. Add the vanilla extract. Beat the egg whites until stiff and fold into the cake mixture.
Divide the mixture between 12 paper cases or greased muffin cups. Top each muffin with half an apricot, rounded side upwards.
Bake at 175°C (fan oven 150°C) for about 20 minutes.
Dust lightly with Siúcra/McKinney's Icing Sugar before serving.