Heat the oven. Preheat the oven to 400°F.
Make the dough. Add the flour, sugar and salt to a food processer fitted with a standard blade. Pulse 2-3 times. Add the butter and pulse again 5-6 times until a small meal forms. With the motor running slowly add the water and process until a ball forms.
Chill the dough. Remove the dough from the food processor and press into a thick round, about 1 ½ inches thick, with the palm of your hand. Cover and chill for about 30 minutes.
Make the apple filling. While the dough is chilling Combine the sliced apples, flour, sugar, cinnamon, nutmeg, cloves and lemon juice in a mixing bowl. Stir until the apple slices are thoroughly coated.
Roll the dough. Place the chilled dough on a large piece of parchment paper (just slightly smaller than your baking sheet). Roll the dough out into a somewhat circular shape until the dough is about ¼ inch thick. Transfer the rolled dough to the baking sheet.
Assemble the galette. Arrange the apple mixture in the center of the dough, leaving a border about 3 inches wide. Fold the edges over the apple mixture, pleating as needed. Combine the egg and water in a small bowl and brush the folded edges of the galette with the egg wash.
Bake the galette. Bake for 30-35 minutes or until the crust is golden brown. Remove from oven and cool for about 5 minutes. Drizzle with caramel sauce and serve.