In a 10 inch cast iron skillet, melt 3 T. butter and 1/2 C. of brown sugar. Stir over low heat until it begins to dissolve into a smooth caramel, then spread the caramel over the pan evenly. Arrange the peach slices in a single layer. Set the pan aside.
To make the cake, cream 1/2 C. each butter and sugar together until light and fluffy. Add 2 beaten eggs, 3/4 C. buttermilk or plain yogurt, 2 T. vanilla extract, and the sweet corn.
In a bowl, combine 1 C. cornmeal and 1 1/4 C. flour with 1 1/4 T. baking powder and 1/4 t. each baking soda and salt (if using unsalted butter).
Mix the liquid and dry ingredients together using as few motions as possible.
Spoon the batter over the peaches and smooth out. Bake for 25-30 minutes. The top of the cake should be golden brown. Let the cake cool for at least 20 minutes before turning the flipping the pan onto a plate and removing the cake.