Preparation
Preheat the oven to 350 F. Place half of the butter in a 9-inch springform cake pan. Place the pan in the oven for 2 minutes to melt the butter. Spread the melted butter evenly over the bottom of the pan, and then sprinkle the brown sugar evenly over the butter. Place the persimmon slices in overlapping concentric circles on the mixture, and then set the pan aside. In a medium bowl, combine the flour, baking powder, baking soda and salt and whisk to mix. In a stand mixer or a bowl with an electric mixer, beat the remaining half stick of butter until creamy. Add the sugar and beat until light and fluffy, about 2 minutes. Beat in the eggs until smooth, scrape down and beat briefly. Beat in the flour mixture, and when the flour is just incorporated, beat in the yogurt until smooth. Dollop the batter evenly over the persimmon, spreading it evenly to the edges of the pan. Bake for 30-35 minutes, until a toothpick inserted in the center of the cake comes out with no wet batter attached. Cool the cake for 5 minutes on a rack, then run a thin knife around the cake to loosen. Remove the pan. Place a plate on top of the cake and use hot pads to hold the plate tight to the cake as you flip to invert the cake. Carefully remove the bottom of the pan.
