Position a rack in the middle of the oven and preheat the oven to 350 degrees F.
For the caramel peaches: Butter a 9-inch cake pan, line the bottom with parchment paper and brush the paper with butter.
Combine the sugar, corn syrup, allspice if using and 1 tablespoon water in a medium saucepan. Cook over medium heat, stirring, until the sugar dissolves. Increase the heat to high and 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, keeping their skins intact. Cut each half into 3 wedges. Arrange the wedges in concentric circles over the caramel in the pan. Sprinkle the bourbon if using over the top of peaches. Set aside.
For the cake: Whisk together the flour, cornmeal, baking powder, baking soda and salt in a medium bowl.
Beat the butter and sugar in a large bowl with a hand-held electric mixer on low speed, about 1 minute. 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 the first to be fully incorporated before adding the second. Reduce the speed to low and add the flour mixture in 3 additions, alternating with the sour cream in 2 additions, beginning and ending with the flour mixture. Increase the speed to medium and mix briefly to make a smooth batter.
Pour the batter over the peaches and smooth the top. Bake the cake until golden brown and a toothpick inserted in the center comes out clean, 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 vanilla ice cream or whipped cream if using.