Preheat the oven to 160°C. Line the bottom of a 23-cm non-stick cake tin (preferably a spring-form tin) with a circle of greased baking paper.
Cut the plums in half, along their seams. Remove the pips, using the point of a sharp knife, and set aside.
Sift the flour, baking powder and salt on to a plate. Put the butter, caster sugar, eggs, almonds, almond extract and milk into a food processor fitted with a metal blade. Turn on the processor, and whizz the mixture together for a minute. Now open the top of the food processor and tip in the sifted flour/baking powder/salt mixture. Whizz, on a high speed, for another minute. Don’t worry if the mixture looks slightly curdled: all will come right in the baking.
(If you don’t have a food-processor, simply combine all the ingredients in a large mixing bowl, using a large balloon whisk.)
Pour the batter into the prepared baking tin. Press the halved plums, cut side up, into the batter. It doesn’t matter how far you sink them in – they will all end up at the bottom of the pan. Tap the cake tin sharply on the counter a few times to pop any air bubbles. Place in an oven heated to 160°C and bake for an hour and twenty minutes, or until the cake is pulling away from the sides of the tin, and an inserted skewer comes out dry.
In the meantime, put the flaked almonds into a dry frying pan and toast, over a medium heat, until they’re just beginning to turn golden brown. Remove from the heat and set aside.
Take the cake out of the oven, allow to cool for five minutes, and then run a sharp knife around the edges of the tin to release the cake. Invert the cake onto a plate, flip off the metal bottom of the cake tin, and peel off the baking paper. Turn the cake the right side up again. Put the icing sugar into a tea-strainer (or sieve), and generously dust the top of the cake with it. Sprinkle the toasted almonds over the cake.
Serve warm, with whipped cream.