Melt the butter in a medium saucepan over low heat. Add the sugar and whisk until well blended. Pour the mixture into a 9-inch round cake pan with 2-inch-high sides, spreading it to evenly cover the bottom of the pan.
Lightly press the plums into the syrup in a circle along the edge of the pan. Spread the berries in the center of the pan. (You can set the pan aside to stand at room temperature for up to 3 hours.)
Make the cake
Preheat the oven to 350°F (176°C) and position the oven rack to the center position.
Sift the flour, baking powder, cinnamon, and salt into a bowl.
In another bowl, beat the butter until smooth. Gradually add the sugar to the butter and beat until well combined. Add the eggs, 1 at a time, beating well after each addition. Beat in the vanilla.
Stir the dry ingredients and the milk alternately into the butter mixture in 3 additions, beginning and ending with the dry ingredients. Spoon the batter over the topping in the pan.
Bake the cake until the top is golden and firm and a tester inserted in the center comes out clean, about 55 minutes.
Let the cake cool in the pan on a wire rack for about 10 minutes.
Run a small sharp knife around the sides of the pan to loosen the cake. Place a plate or platter over the pan. Using oven mitts or pot holders, firmly grasp the pan and platter together, then turn them over. Let stand 3 minutes, then gently lift the pan off the cake.
Serve the cake warm or at room temperature with ice cream or whipped cream, if desired. The cake is, as most cakes, best served the day it is baked.