Preheat oven to 350°F/180°C. Grease or line a 20 cm (8 inch) round cake pan.
In a mixing bowl, cream together softened butter and sugar until light and fluffy.
Add eggs, sourdough starter, buttermilk, cream cheese (or yogurt), vanilla and mix until smooth.
In another bowl, whisk together flour, baking powder, baking soda, and salt. Fold dry ingredients into wet mixture with a spatula until just combined. Do not overmix.
Pour melted butter into the prepared cake pan and swirl to coat the bottom. Sprinkle evenly with brown sugar.
Arrange plum slices in a single layer over the sugar.
Gently spread the cake batter over the fruit.
Bake for 40–45 minutes, or until a toothpick inserted in the center comes out clean.
Allow to cool slightly before inverting onto a plate. Serve warm or at room temperature.