Position a rack in the middle of the oven and preheat to 350 degrees F. Butter a 9-inch cake pan, line bottom with parchment paper and brush the paper with butter.
Caramel peaches: Combine the sugar, corn syrup, allspice and water in a medium saucepan. Stir over medium heat until the sugar dissolves. Increase the heat to high, and continue to cook, without stirring, until the mixture becomes an amber caramel, about 5 minutes. Pour the caramel into the prepared pan and set aside to cool.
Halve and pit the peaches, but leave their skins on. Cut each half into 3 wedges. Arrange the wedges in concentric circles in the pan. Set aside while you make the cake batter.
Cake: Whisk the all-purpose flour, white corn flour, baking powder, baking soda, and salt in a medium bowl.
Slowly mix the butter and sugar in a large bowl with a hand-held electric mixer. Increase the speed to high, and continue beating until the butter is light and fluffy, about 5 minutes. Add the eggs 1 at time, waiting for each to be fully incorporated before adding the next.
While mixing at a low speed, add the dry ingredients in 3 additions, alternating with the sour cream in 2 additions, beginning and ending with the flour. Increase the speed to medium and mix briefly to make a smooth batter. Pour the batter over the peaches and smooth over.
Bake the cake until golden brown and a toothpick inserted in the center comes out clean, about 40 to 45 minutes. Cool the cake in the pan on a rack, about 20 minutes.
Run a knife around the edge of the pan to release the cake. Carefully invert the cake onto a serving plate and remove the parchment paper. Serve warm or at room temperature with ice cream or whipped cream, if desired.
Serving suggestions: Vanilla ice cream or whipped cream.
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