Preheat an oven to 425 degree F.
On a lightly floured work surface, roll out the puff pastry into a 16-by-14-inch rectangle. Carefully roll the pastry around your rolling pin and transfer it to a 9- or 10-inch ovenproof cast iron pan, pressing it gently into the bottom and up the sides of the pan. Refrigerate while you prepare the filling.
In a food processor, combine the almonds, sugar and salt and process until the almonds are finely ground. Add the eggs, vanilla and almond extracts and the melted butter and process until the mixture comes together. Set aside.
In a bowl, toss the apple slices with the lemon juice to coat.
To assemble the galette, pour the almond mixture into the pastry-lined pan and spread evenly. Arrange the apple slices evenly on top of the frangipane, overlapping them slightly. Fold the excess puff pastry back over the edges of the pan to form a rim or crimp the pastry decoratively. Brush the pastry with the egg wash.
Bake until the pastry is golden brown and the apples are tender, 40 to 45 minutes. Serve warm or at room temperature with a scoop of ice cream and salted caramel sauce on top. Serves 8.