To make the dough, combine flour, sugar, cornmeal, and salt in a processor; pulse 2-3 times. Add butter and pulse 4-5 times, or until mixture resembles coarse meal.

With the processor running, slowing pour the buttermilk through the chute, processing until the dough forms a ball. Remove the dough ball and adhere any remaining pieces of dough to it, then wrap in plastic wrap or parchment paper. Refrigerate for at least 45 minutes before rolling out.

Preheat the oven to 375 degrees F.

Remove the galette dough from the refrigerator and place on a sheet of parchment paper while you make the apple filling.

Put the apple slices in a large bowl. Drizzle the lemon juice over the apples and toss. Add the brown sugar, cornstarch, cinnamon, vanilla, and ground allspice, if using. Stir until the apples are well coated. Set aside.

Starting at the center of the dough, roll out, forming a 14-inch-wide circle. Place the dough with parchment paper on a large baking sheet.

Arrange the apple slices on top of the dough, leaving a 2-inch border, leaving the excess juices in the bowl so the galette doesn’t get soggy. Fold the dough border gently over the apples, overlapping where necessary and pressing gently to adhere the folds. You can brush the apple with a little bit of the juice.

In a small bowl or ramekin, beat the egg with a splash of water. Lightly brush the edge of the dough with the egg. In a small bowl, combine the turbinado sugar and cinnamon. Sprinkle the cinnamon sugar over the galette crust.

Bake the galette for 40-45 minutes, or until the crust is golden brown. Transfer the baking sheet to a wire rack to cool to room temperature before slicing.

Cut into wedges and serve with salted caramel sauce and vanilla ice cream, if desired.