Preheat the oven to 180C/350F/Gas 4. Grease and line two 8-inch cake tins.
In a large bowl, beat the butter and sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Fold in the flour and baking powder, then add the milk and mix until smooth.
Divide the mixture evenly between the prepared tins and smooth the tops.
Bake for 20-25 minutes, or until a skewer inserted into the center comes out clean.
Leave to cool in the tins for 5 minutes, then turn out onto a wire rack to cool completely.
For the filling, beat the butter until smooth and creamy, then gradually beat in the icing sugar and vanilla extract.
Spread the buttercream over the bottom of one of the sponges. Spread the jam over the bottom of the other sponge.
Sandwich the two sponges together and dust the top with icing sugar.