Preheat the oven to 170C/325F/Gas 3. Grease the sides of a 20cm/8in cake tin and line the base with greaseproof paper.
Cream the butter in a large bowl or an electric food mixer until soft. Add the sugar and beat until the mixture is light and fluffy. Gradually add the beaten eggs, beating well between each addition.
Sift in the flour and baking powder, add the poppy seeds and stir until well combined.
Spoon the mixture into the prepared cake tin and smooth the surface with the back of a spoon. Bake in the oven for 25-30 minutes, or until it is cooked in the centre and a wooden skewer inserted into the middle comes out clean.
Remove from the oven and allow the cake to stand for five minutes before carefully removing it from the tin and transferring it to a wire rack to cool.
For the buttercream icing, using an electric whisk, beat the butter until pale and soft. Beat in the icing sugar and vanilla extract.
When the cake is cool, cut it in half using a long, serrated knife. Place one layer of the cake on a serving plate and spread over two generous tablespoons of the vanilla buttercream, then place the other half of the cake on top.
Spread the remaining icing over the top and sides with a palette knife.