Put the butter and sugar in a mixing bowl and beat together with a wooden spoon until pale and creamy. Gradually beat in the eggs and vanilla extract, a little at a time, adding 1 tablespoon of flour with each addition – this will help to prevent the mixture from curdling.
Sift the remaining flour and baking powder into the bowl and fold gently into the creamed mixture.
Divide the mixture between two lightly oiled 18 cm (7 inch) sandwich tins that have been lined with a circle of greaseproof paper or non-stick baking paper. Spread the tops level, then bake in a preheated oven at 180°C (350°F), Gas Mark 4, for about 20 minutes or until the cake will spring back when lightly pressed with a fingertip. Leave to cool for 5 minutes, then loosen and turn the cakes out on to a wire rack, peel off the lining paper and leave to cool.
Put one of the cakes, top downwards on to a serving plate, spread with the jam, then top with the second cake. Dust the top with sifted icing sugar and cut into slices to serve.