Make the pastry by hand: Add the flour, cornmeal, salt, sugar and butter to a mixing bowl. Using two knives or a pastry cutter, cut in the butter until it resembles course sand. Add the water and mix it all together until the dough comes together. OR pastry with a food processor: Add the flour, cornmeal, salt, sugar and butter to a food processor. Pulse until the mixture resembles course sand. Add the water and continue to pulse until the dough comes together.
Form into balls and chill: Turn the dough over onto a floured surface and form it into a ball. Cut the ball into 2 pieces, and flatten each one into a disk. Wrap in plastic wrap and refrigerate for at least an hour.
Make the filling: In a large bowl, mix the apples, brown sugar, flour and lemon juice.
Prep the oven and baking sheet: Preheat oven to 375°F. Line a large baking sheet with parchment paper.
Shape and assemble: When the dough has chilled, roll each piece into a rough circle, that's maybe about 12 inches in diameter. In the middle of each circle, place 1/2 of the apple filling. Leave about a 2 to 3 inches border. Slowly fold up the sides of the galette over the apples all the way around. Repeat this with the remaining pastry and filling. In a small bowl combine brown sugar with the ground cinnamon and sprinkle over the galettes. Brush the pastry crust with the beaten egg.
Bake: Transfer the baking sheet to the oven and bake for about 30 to 35 minutes or until golden brown.