Preheat the oven to 350 degrees F (175 degrees C). Grease a 9-inch cake pan. Combine flour, baking powder, and salt; set aside.

Combine brown sugar and 3 tablespoons butter in the prepared pan. Place pan inside the preheated oven until butter melts and begins to bubble; set aside.

Beat 1 cup white sugar and 1/3 cup butter in a large bowl with an electric mixer until light and fluffy. Beat in egg, then stir in vanilla. Beat in flour mixture, alternately with milk, mixing just until incorporated.

Arrange plums around the edges of the prepared pan, overlapping slightly. Distribute blueberries in the center. Pour batter into prepared pan, covering fruit completely.

Bake in the preheated oven for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool 15 minutes before serving.