Preheat the oven to 220°C/425°F/gas mark 7. Sift the flour, baking powder, salt and caster sugar into a bowl. Cut the butter into small pieces, add to the flour and crumble with your fingers, as though making pastry, until the mixture is like fine breadcrumbs. In a measuring jug, whisk the egg and vanilla essence together and add enough milk to make it up to 125 ml/4 fl oz. Add to the flour and butter mixture and stir thoroughly. Spoon the batter into a buttered rectangular dish measuring about 25 x 20cm/10 x 8in.
For the topping, peel and core the apples, then slice them thinly and arrange in closely overlapping rows on top of the cake mixture. Melt the butter in a pan, stir in the sugar and cinnamon and spoon evenly over the apples. Bake in the centre of the oven for 25 minutes, until risen and browned.