1. Preheat the oven to 350 degrees F. Grease the bottom and sides of a 9 inch springform pan. Set aside.
2. Sift the flour, baking powder, cinnamon and salt into a large bowl. Add 1/2 cup of the cornmeal and whisk together to combine.
3. Put the butter and sugar into the bowl of a stand mixer. Beat on medium speed until light-colored and fluffy, about 3 minutes. Add in the eggs one at a time and mix until combined. Add in the vanilla extract and mix.
4. Add the flour mixture and the buttermilk to the mixer bowl in additions, starting and ending with the dry ingredients. Beat just until all the ingredients are combined.
5. Spread about half of the mixture into the springform pan, spreading evenly. Place about half of the plum pieces over the batter. Spread the remaining batter into the springform pan and top with the rest of the plums. Sprinkle the 1 tablespoon of cornmeal over the top of the batter. Sprinkle turbinado sugar over the entire cake.
6. Bake for about 50 minutes or until a tester inserted into the center of the cake comes out clean. Let cake cool in the pan for 15 minutes. Gently remove the cake from the pan and serve.