Preheat oven to 400 degrees. In a medium bowl, whisk together flour, cornmeal, baking powder, baking soda, salt, and granulated sugar. Using the large holes on a box grater, grate butter into flour mixture. Using your fingers, incorporate butter into flour mixture, breaking it into even smaller pieces. With a fork, stir in buttermilk until dough just comes together. Lightly flour a rolling pin and work surface and roll out dough to a 3/4-inch-thick rectangle. Cut into 6 squares (or rectangles).
Place dough squares, 3 inches apart, on a parchment-lined baking sheet. Brush tops with buttermilk and sprinkle with granulated sugar. Bake until shortcakes are golden and puffed, 17 to 20 minutes. Let cool completely on a wire rack.
In a medium bowl, using an electric mixer, beat cream and confectioners' sugar on high until stiff peaks form, about 3 minutes. Cut shortcakes in half horizontally. Divide peaches among bottom halves, top with whipped cream and blueberries, and sandwich with top halves.
A box grater is the perfect tool for getting the butter into small pieces. Make sure your butter is very well chilled before you start. Swap It: Be flexible with the fruit in all these desserts. Use peaches in place of nectarines, or a mixture. Store plain shortcakes, tightly wrapped in plastic, up to 2 days.