Preheat the oven to 180C. Grease and line a 23cm square (or round, for a deeper cake) cake tin. Cut each apricot in half again and place in a bowl with ¼ cup of the measured caster sugar and toss to coat. Set aside.
Cream the butter and remaining caster sugar until light and creamy. Add the eggs, one at a time, beating well between each addition. Add the vanilla.
Sift the flour and baking powder together and fold into the creamed mixture with ½ cup custard. Spoon half of the cake mixture into the prepared tin and arrange half the apricots with their sugar on top. Dollop over the remaining ¼ cup custard then the remaining cake mixture. Finish with remaining apricots, gently pressing them just a little way into the cake mixture.
Place in the oven and bake for 45 minutes. To test, insert a skewer into the centre of the cake; it should come out clean. Leave cake to cool in the tin for about 15 minutes befroe serving warm as a dessert with extra custard and whipped cream. Or, leave until completely cool and serve as a delicious morning or afternoon tea cake. Store in an airtight container for a couple of days in a cool place.