Heat the oven to 350℉. Grease and flour an 8- to 10-inch springform pan.
Sift the flour, baking powder, and salt together. Set aside.
Beat the butter, lemon zest and ¾ cup sugar on medium-high speed in a stand mixer with the paddle attachment until pale and fluffy, about 3 minutes. Stop the mixer to scrape the paddle and insides of the bowl. If you are using a handheld mixer, alter the mixing time depending on its power.
With the mixer off, add the eggs, vanilla and sifted dry ingredients. Mix on low speed until well combined. Scrape the bowl as needed.
Spread the thick batter evenly in the pan. It will seem sparse, especially in a 10-inch pan. Arrange the plums, skin side up, completely covering the surface of the batter. Sprinkle the top with lemon juice, then cinnamon and sugar (a large-grained crunchy kind, if you have it). Place the pan on a baking sheet, or wrap its base in foil to prevent the batter leaking out during baking.
Bake for 40-55 minutes, or until a toothpick inserted in the center comes out clean and the cake top is golden brown. Cool in the pan on a rack for at least 1 hour, then remove the pan sides before serving. It is also excellent after resting at room temperature overnight, and wrapped leftovers keep well for several days.
Exchange up to ⅓ of the flour for almond flour or cornmeal. I often cut the fruit into big wedges that peek up through the batter. Great with apricots, peaches, cherries, berries, pears, & jammy Concord grapes.