1. Step 1: Preheat the oven to 400°F (200°C) and line a 9×13-inch baking pan with parchment paper, leaving a little overhang on the long sides so you can lift the slices out later.

2. Step 2: On a lightly floured surface, roll one sheet of thawed puff pastry into a rectangle that fits the bottom of the pan, then lay it in and gently press it into the corners.

3. Step 3: In a large mixing bowl, combine the sliced apples with the granulated sugar, brown sugar, flour, cinnamon, nutmeg, salt and lemon juice, tossing until every slice is evenly coated.

4. Step 4: Spread the apple mixture evenly over the puff pastry in the pan, making sure the apples reach all the way to the edges, then drizzle the melted butter over the top.

5. Step 5: Roll the second sheet of puff pastry to roughly the size of the pan and place it over the apples, matching the edges and pressing gently to cover the filling.

6. Step 6: Pinch or crimp the edges of the top and bottom pastry together all the way around the pan to seal, then cut several small slits in the top crust with a sharp knife to let steam escape.

7. Step 7: Whisk the egg and water together to make an egg wash, brush it over the top pastry, and bake for 28 to 32 minutes or until the pastry is puffed and deep golden brown and the filling is bubbling.

8. Step 8: Remove the pan from the oven and let the apple slices cool in the pan for at least 45 to 60 minutes, until they are warm but no longer hot, so the filling can thicken.

9. Step 9: In a small bowl, whisk together the powdered sugar, 2 tablespoons of milk or cream and the vanilla, adding a little more milk as needed to reach a thick drizzle, then pour the glaze over the cooled pastry, let it set for a few minutes and cut into 12 squares to serve.