Preheat your oven to 350°F (175°C). Grease an 8-inch round cake pan with butter and line with parchment paper.

Melt 1 tablespoon of unsalted butter in a skillet over medium-high heat. Add sliced firm, ripe plums and 2 tablespoons of granulated sugar. Cook for 3-4 minutes until plums soften.

Pour plums and syrup into the cake pan, arranging plums in concentric circles.

Whisk together 1 ½ cups of flour, 1 teaspoon of baking powder, ½ teaspoon of baking soda, and ½ teaspoon of salt in a bowl.

In a mixing bowl, cream ½ cup of softened unsalted butter and ½ cup of granulated sugar until light and fluffy. Add 1 egg, ½ cup of sour cream, and 1 teaspoon of vanilla extract, mixing until smooth.

Gradually add the dry ingredient mixture to the wet ingredients, mixing gently until just combined.

Pour the batter over the arranged plums in the cake pan and spread evenly. Bake for 50-55 minutes until golden brown.

Allow the cake to cool in the pan for 1 hour. Run a knife around the edges, then invert onto a plate.