Preheat the oven to 180°C.
Grease a rectangular cake pan and line it with baking paper.
Cream the butter and sugar, then add the eggs, one at a time, beating well after each addition. Stir in the vanilla and lemon zest.
Sift the flour into the batter and combine, then transfer it into the cake tin.
Cut the apricots in half and remove the stones. Arrange the apricot halves, cut-side down, on top of the batter.
Bake for 30-35 minutes in the middle of the oven or until a skewer inserted in the middle of the cake comes out clean. Cover the tin with foil if the cake browns too quickly.
Cool the cake in the tin, then transfer it to a wire rack.
When the cake has completely cooled, cut it into squares and dust with icing sugar just before serving.