Preheat the oven to 350 degrees and grease a 9-inch springform pan. (It’s okay if your pan is a little bigger or smaller. You may need to adjust the baking time slightly.)
In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, stir together the eggs, coconut sugar, coconut oil, and coconut milk. Add the dry ingredients to the wet ingredients and mix to combine.
Transfer the batter to the springform pan in an even layer. Cut each plum half into about 4 sections, and arrange the plum pieces on top of the batter. Sprinkle the plums with additional coconut sugar if desired. Line the bottom and sides of the pan’s exterior with aluminum foil so the batter doesn’t leak in the oven.
Bake for 55 to 60 minutes, or until the cake is lightly browned and a toothpick inserted in the center comes out clean. Cool on a wire rack.