Everyone will flip for this stunning dessert crowned with shingled plum slices. The addition of buttermilk to the batter keeps the cake underneath wonderfully moist.
Preheat oven to 350 degrees. In a 9-by-2-inch round cake pan (or a 10-inch cast-iron skillet), melt butter and brown sugar over low heat. Using a fork, mix together until smooth. Remove pan from heat.
Cut plums in half, twisting to pull apart; remove pits and discard. If any flesh clings to pit, place stem-end down and cut on both sides of pit to remove any remaining flesh. Place plum halves, cut-side down, on work surface, and cut into 1/4-inch-thick slices. Transfer each sliced half, skin-side down, to cake pan, fanning slices out in an overlapping pattern so that more of the skin comes in contact with the bottom of the pan, rather than the flesh. Fill in any gaps with slices from around pit.
In the bowl of a mixer fitted with the paddle attachment, beat together butter and sugar until light and fluffy. In a small bowl, beat together egg yolks and vanilla; add to butter mixture. In another small bowl, whisk together flour, baking powder, and salt. With mixer on low, add flour mixture, alternating with buttermilk, beginning and ending with flour mixture; beat until just combined. Transfer batter to a wide bowl.
Clean mixer bowl and return to mixer fitted with the whisk attachment; beat egg whites until soft peaks form. Stir one-third of egg whites into batter. Gently fold in remaining egg whites until incorporated. Pour batter over plums, spreading to cover evenly.
Bake until top is browned and springs back when lightly pressed in center, and a tester inserted into cake comes out clean, 50 minutes to 1 hour. Let cake cool in pan 20 to 25 minutes, then carefully invert onto a cake plate; let cool completely.
You can also use fresh blueberries to fill in any gaps in step 2.