Preheat oven to 425°F. Line a large rimmed baking sheet with parchment paper; set aside. Stir together flour, cornmeal, baking powder, salt, baking soda, and 3 tablespoons of the granulated sugar in a large bowl. Using a pastry blender or 2 forks, cut in cold butter until mixture is crumbly. Stir in cold buttermilk until a shaggy dough forms.

Turn out dough onto a lightly floured work surface. Pat dough into a rectangle, and cut into fourths.

Stack each fourth on top of each other, and pat down into a rectangle again. Repeat process 3 times.

Pat or roll dough to 1-inch thickness (about a 6- x 9-inch rectangle). Trim edges; cut dough evenly into 6 (about 3-inch) squares. Arrange biscuits 2 inches apart on prepared baking sheet. Freeze until cold, about 10 minutes.

Remove biscuits from freezer; brush evenly with egg. Bake in preheated oven until golden brown, 13 to 15 minutes. Remove from oven.

While biscuits bake, hull and quarter strawberries, if using. Stir together mixed berries, lemon juice, and remaining 3 tablespoons granulated sugar in a medium bowl until combined. Let stand until macerated, stirring occasionally, about 10 minutes.

Beat cream, powdered sugar, lemon zest, and vanilla bean paste with an electric mixer on high speed until soft peaks form, about 2 minutes. Split biscuits horizontally. Dollop evenly with whipped cream, and spoon macerated berries evenly over tops.