Preheat oven to 350°. Cut a piece of parchment paper into a 9" round to fit the bottom of a 9" x 2" cake pan. Spray the pan liberally with vegetable spray. Place the parchment in the bottom of the pan and spray again. Set aside.
Slice the plums into 6-8 wedges each and transfer to a bowl. Sprinkle with sugar and toss to coat. Set aside.
In a medium bowl, combine the flour, cornmeal, baking powder, baking soda, salt, and cinnamon. Whisk to combine and set aside.
In a large mixing bowl beat the butter, sugar and brown sugar until creamy - 2-3 minutes. Add eggs one at a time, beating each one in before adding the next. Add the vanilla and mix to combine.
In two additions, alternate adding the flour and buttermilk to the sugar mixture. Don't overmix.
Spread 2/3 of cake batter evenly in the prepared pan. Arrange the plums in concentric circles starting at the edge and working your way around the pan. Dollop the remaining batter over the plums (it doesn't need to completely cover them). Sprinkle with turbinado sugar (if using) and bake for 50-60 minutes or until a toothpick comes out clean.
Cool the cake on a wire rack until it reaches room temperature. Carefully turn the cake out onto a plate and flip it over so the top side is up. Serve with whipped cream or a scoop of vanilla.