Place a rack in the center of the oven, and preheat the oven to 350 degrees F.
Pour the melted butter in the bottom of a 9-inch square pan. Sprinkle with the brown sugar and lemon juice. Place 9 of the peach halves, cut-side down, in the pan, pressing them close together into the sugar mixture. Finely chop the remaining peach half and set it aside.
For the cake, place the corn meal and sugar in a large bowl. Whisk in the melted butter, eggs, vanilla, and milk. Fold in the reserved chopped peaches. Pour the batter over the peach and sugar mixture. Place the pan in the oven.
Bake until the cake is golden and springs back, about 45 to 50 minutes. Remove the pan from the oven, and let the cake rest 5 minutes. Run a knife around the edges of the cake, and invert it onto a serving plate. Let cool before serving with whipped cream.