Position a rack in the middle of the oven. Heat the oven to 350 degrees F. Oil a 9-inch springform cake pan with olive oil and dust with sugar. Arrange the plums in a single layer on the bottom of the pan.

In the bowl of a stand mixer, combine the cake flour, baking soda, salt, and 1/2 cup of the sugar. In a small bowl, combine the buttermilk, olive oil, vanilla, and egg yolks. Stir the mixture lightly with a fork.

With the mixer on low speed, gradually pour the liquids into the dry mixture to make a smooth batter, 1 to 2 minutes. Add the lemon zest and lemon juice and combine briefly again, scraping down the sides of the bowl at least once. If any lumps remain, increase the speed to medium for about 30 seconds to smooth them out. Set the batter aside.

In another large stand mixer bowl (transfer the cake batter to another bowl if you have only one), whip the egg whites on medium speed until they form soft peaks, about 2 minutes. Increase the speed to high and gradually add the remaining 1/4 cup sugar in a steady stream, scraping down the sides of the bowl after all the sugar has been added. Continue whipping the whites until they're very stiff, about 3 minutes.

Pour about half of the reserved cake batter over the whites and, using a whisk, gently stir it in by hand until the batter is lightened but not quite blended, just a few strokes. Pour in the remaining batter and gently whisk it in until it's well incorporated and there are no white streaks. Pour the batter into the prepared pan with the plums. Put the blueberries in a small bowl, toss them gently with the 1 teaspoon flour, and then scatter them over the batter. Bake until a toothpick inserted in the center comes out clean, 50 to 60 minutes. Cool the cake on a rack for 10 minutes and remove the ring. Cool the cake another 5 minutes and turn it over onto another rack or plate. Very slowly lift off the pan base, inch by inch, nudging loose any resisting fruit with a spatula. Let the cake cool before transferring it to a serving plate.