In a food processor, combine the butter, sugar, eggs, milk, and vanilla and process until smooth. Add all three flours, the baking powder, and salt and mix together by pulsing several times, just until smooth.
Scrape the batter into the prepared pan and smooth the top with a spatula. Gently tap the pan on the counter several times to release excess air bubbles. Add the plums in a spiral on top of the batter. Set the pan on a baking sheet.
Bake for about 45 minutes. To make the topping: in a small bowl, mix together the sugar and cinnamon.