Preheat oven to 400 degrees. Butter and flour an 11-inch round tart or quiche pan.
Whisk flour, baking powder, cane sugar, and salt in a large bowl. In a separate bowl, whisk eggs and buttermilk. Whisk in the melted butter and lemon zest. Add butter-and-buttermilk mixture to flour mixture and stir gently until just combined.
Pour batter into prepared pan and smooth top with a spatula. Arrange plums across the top. Sprinkle with turbinado sugar.
Bake for 25 to 30 minutes, or until cake has set and a toothpick inserted in center comes out clean. Serve warm or at room temperature.
You can also make this cake in a 9-by-13-inch rectangular baking dish. Check cake for doneness at 20 minutes.