1. Preheat oven to 350F. Butter a 9-inch cake pan, line with parchment paper, and butter parchment paper.
2. For Peaches: Stir sugar, corn syrup, allspice berries, and water in a medium saucepan. Cook, stirring continually, over medium heat, until sugar dissolves. Increase heat to high and cook, without stirring, until mixture turns an amber caramel, about 5 minutes. Remove from heat and discard allspice. Pour caramel into pan and cool. Cut peaches into wedges and arrange in concentric circles on caramel. Set aside.
3. For Cake: Whisk flour, cornmeal, baking powder, baking soda, and salt in a medium bowl. Beat butter and sugar in a large bowl with an electric mixer on high speed until light and fluffy, about 5 minutes. Beat in eggs, one at time. Reduce speed to low. Add dry ingredients in 3 additions, alternating with sour cream, and beginning and ending with dry ingredients. Increase speed to medium and mix until batter is smooth, about 20 seconds.
4. Spread batter evenly over peaches and bake until cake is golden brown and a toothpick inserted in center comes out clean, about 40 to 45 minutes. Cool cake for 20 minutes, in pan, on a rack.
5. Slide a knife around edge of cake pan, invert pan onto a serving plate, and release cake. Remove parchment paper. Serve warm or at room temperature.
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