Preheat the oven to 350F (175C), and position a rack in the center. Line the bottom of a 10-inch (25 cm) spring-form pan with baking parchment. Grease the sides and bottom well with baking spray or butter. Set aside.

In a medium bowl, whisk together the flour, baking powder, salt, lemon zest,  and cinnamon. Set aside.

With an electric mixer, beat the egg and the sugar on high speed until the mixture is creamy, pale yellow, and lighter in volume, about 5 minutes. With the mixer on low, add the olive oil, then the milk and balsamic vinegar. Fold in the flour mixture with a rubber spatula just until it makes a smooth batter.

Scrape the batter into the prepared pan. It will look really skimpy once it's in the pan, but don't worry. Arrange the plums in a single layer across the batter, and sprinkle the cake with the sugar.

Bake for 50 to 55 minutes, until the cake is golden brown on top, a little puffed, and set in the center (a toothpick should come out free of batter but may have a few crumbs clinging to it). Cool on a wire rack for 5 minutes, then remove the sides and cool until just barely warm. You can serve it either that way, or at room temperature.