Preheat oven to 400ºF.

In a large mixing bowl whisk together the flour, cornmeal, sugar, baking soda, baking powder and salt. Add the butter to the bowl and use a pastry cutter or a fork to cut the butter into the flour. Do this until the mixture resembles rough crumbs and the butter is still in pieces. Add the buttermilk and stir with a wooden spoon until loose, sticky dough forms.

Turn the dough out onto a clean, lightly floured surface. Use your hands to shape the dough into a rectangle. Fold the dough over and reshape again into a rectangle about 1½-inches thick. Cut the dough into biscuits by pressing straight down, using a 2-inch biscuit cutter. Reshape the dough as needed to continue cutting biscuits.

Place the biscuits on a greased cookie sheet and brush with the beaten egg. Sprinkle with the demerara sugar and bake until golden brown, about 12 to 15 minutes. Remove and let cool on a baking sheet.

Sprinkle the halved peaches with half the sugar and let sit for 15 to 20 minutes. Sprinkle with the remaining sugar and using a torch, slowly caramelize the sugar until its golden brown and bubbling, about 2 minutes.

Add the heavy cream to the bowl of a stand mixer fitted with the whisk attachment and beat on medium speed for 1 minute. Keep the mixture running while you add the sugar then increase the speed of the mixer to medium-high, beating until the cream forms stiff peaks, about 2 minutes. Cover and refrigerate until ready to use.

Split the biscuits and add to a bowl with the caramelized peaches. Top with whipped cream and basil.