Preheat oven to 350 degrees F. Coat bottom and sides of 13X9X2-inch glass baking dish with nonstick vegetable cooking spray.
To peel the peaches, bring a medium saucepan of water to a boil. Make sure the water is deep enough to totally submerge a peach. Cut a small X in the bottom of every peach (about ½-inch long). Lower each peach into the boiling water for 15-30 seconds, then lift out and drain. Transfer to bowl. Remove the peach skin and slice thinly when ready to top the batter.
Whisk the flour, baking powder, salt, and baking soda in a medium bowl.
Beat the butter in a large bowl with an electric mixer until smooth. Gradually mix in the sugar and beat until light and fluffy. Beat in the vanilla extract. Add the eggs one at a time, beating to mix well after adding each one.
With the mixer on low speed, add the flour in 3 steps, alternating with the buttermilk, beating well and scraping the bowl after each addition.
Pour batter into the prepared baking dish, spreading it evenly. Place the peach slices atop the batter in close rows, overlapping them if necessary. Coat the dull side of a piece of aluminum foil larger than the baking pan with the nonstick spray. Cover the baking dish with the foil, sprayed side down. Seal tightly around the edges of the baking pan.
Bake for 45 minutes. Remove the aluminum foil (and don’t worry if a bit of cake sticks to it). Return the baking pan to the oven and bake and additional 25-40 minutes. The top will become golden brown, the edges will be browner, and a toothpick inserted into the center of the cake will come out clean.
Cool the cake in the pan for 1 hour. Slice and serve warm with the whipped cream topping.