Preheat oven to 325 degrees F. Set your baking rack on the middle shelf in the oven. Prepare a springform pan for your cake by lightly spraying it with an oil spray and then dusting the pan with flour (tapping off the excess).

Combine the dry ingredients (flour, 1/2 C. sugar, baking powder, salt) in the bowl of a stand mixer and mix briefly. Keep your mixer running and add the butter one piece at a time. Continue to mix the ingredients until the flour takes on the consistency of moist sand. This will take 3-4 minutes. Add the egg and egg yolk to the flour. Add the vanilla. Beat this mixture at medium-high speed until it is pale and fluffy. This will take about 1 minute. You can scrape down the sides of the bowl as you are doing this to be sure that you are incorporating all the ingredients.

Spread the batter across the bottom of your prepared springform pan using an offset spatula. Then, arrange the sliced plums in concentric circles across the top of the batter. The cut sides of the plums should face up. Sprinkle the remaining 2 T. sugar on top of the cake and put the cake into the oven to bake. Bake until the cake is golden brown and a skewer inserted in the center of the cake comes out clean. The original recipe called for baking the cake about 1 to 1 1/4 hours but my cake was perfectly done after one hour. Remove the baked cake from the oven and let it cool on a wire rack for about 30 minutes, after which you can remove the sides of the springform pan.

Dust with powdered sugar and serve warm.