Heat oven to 350°F (175°C). Grease and line a 9-inch springform pan.
In a bowl, whisk flour, baking powder, baking soda, and salt.
In another bowl, cream butter and sugar until fluffy. Add eggs one at a time, then vanilla.
Stir in sour cream. Gradually add dry ingredients until just combined.
Spread batter into the pan. Arrange sliced plums on top, pressing gently into the batter.
Bake 40–45 minutes, until golden and a toothpick comes out clean.
Dust with powdered sugar. Serve warm or at room temperature.