Set the oven at 180C/355F/Gas 4. Line the base of a round 20cm cake tin, about 6cm deep, with a piece of baking parchment.
Beat the butter and sugar until pale and fluffy. Whilst this is happening, halve the plums, remove the stones and cut each half in two.
Beat the eggs lightly with a fork, and then add them bit by bit to the butter and sugar. Sift the flour and baking powder together and fold them gently into the mixture. Fold in the ground almonds.
Scrape the mixture into the lined cake tin. Place the quartered plums on top of the cake mixture.
Bake for forty minutes, and then test with a skewer. If it comes out clean, without any wet cake mixture sticking to it, then the cake is ready. Remove the cake from the oven and leave to cool in the tin for fifteen minutes before turning out.