Preheat oven to 350°F.
In a bowl of your stand mixer cream the butter, sugar, salt and baking powder on high speed until light and fluffy, be sure to stop the mixer and scrape up the sides of the bowl. Add the eggs, one at a time, and beat on medium speed until smooth.
Stop the mixer and sift all of the flour into the bowl. Mix on low speed until the batter is just incorporated, not any longer. Pour the batter into an ungreased 9-inch springform pan.
Arrange the plums (and peaches, if using) skin side up over the cake. Sprinkle the cake with cinnamon, lemon juice and 2 TBSP sugar.
Bake in preheated oven for 40-50 minutes (mine was ready right at 40 minutes) until the toothpick comes out clean. The internal temperature should be around 204-206° (with a digital thermometer inserted into the middle of the cake, avoiding touching the bottom of the pan.) Just be sure to avoid 212°F and beyond, since that's the temperature that water turns to steam, which means you'll start losing precious moisture fast.
Cool before serving.
This cake tastes even better the next day.
It will seem like there is very little batter. But the cake will rise as it bakes and the proportion of batter to fruit is simply perfect.
Do not grease the pan, this will prevent the cake from rising properly.