Melt 3 tablespoons butter in a 10-inch cast-iron skillet over medium heat, using a pastry brush to coat the sides with the butter. Sprinkle 1/4 cup sugar evenly over the bottom of the skillet and cook until the sugar starts to bubble and turn golden brown, about 3 minutes. Arrange the peaches in a circle at the edge of the skillet on top of the sugar. Arrange the remaining wedges in the center to fill. Reduce the heat to low and cook until the juices are bubbling and the peaches begin to soften, 10 to 12 minutes. Remove from the heat.
Whisk the cornmeal, flour, salt and baking powder in a medium bowl. Beat the remaining stick of butter and 3/4 cup sugar with a mixer on high speed until pale and fluffy, about 3 minutes. Reduce the speed to medium. Add the eggs, one at a time, beating well after each addition and scraping down the sides of the bowl. Mix in the vanilla extract and 1/2 cup heavy cream. Reduce the speed to low and beat in the cornmeal mixture in two additions.
Drop large spoonfuls of the batter over the peaches and spread evenly using an offset spatula. Bake until golden brown and a tester inserted in the center comes out clean, 20 to 22 minutes. Transfer the skillet to a wire rack and let stand for 10 minutes.
Run a knife or spatula around the edge of the cake. Invert the cake onto a cutting board. Tap the bottom of the skillet to release the peaches and carefully remove the skillet. Reposition the peach slices on top of the cake. Let cool slightly before serving.