Prepare your workspace and ingredients. Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper. Take the puff pastry out of the refrigerator about 15 minutes before you plan to use it so it’s easier to work with.
Core and slice the apples thinly. Aim for slices about ⅛-inch thick, and place them in a medium bowl. Immediately toss with lemon juice to prevent browning.
Mix the flavor components. In a small bowl, combine the granulated sugar, brown sugar, cinnamon, nutmeg, and flour. Sprinkle this mixture over the apple slices and gently toss until evenly coated.
Prepare the pastry base. Unfold the puff pastry sheet onto the lined baking sheet. Using a knife, score a 1-inch border around the edge without cutting all the way through the pastry. This creates a frame that will puff up around your filling.
Arrange the apples attractively. Place the sugar-coated apple slices inside the scored border, slightly overlapping them in rows or a circular pattern. Don’t pile them too high as this can make the center soggy.
Create the egg wash and apply. Beat the egg with 1 tablespoon of water and brush it on the border of the pastry (not on the apples). This will give your pastry that professional golden-brown finish.
Bake until perfectly golden. Place the baking sheet in the oven and bake for 25-30 minutes, or until the pastry is puffed and golden brown and the apples are tender.
Add the finishing touches. If using, warm the apricot jam or honey in the microwave for 10-15 seconds until fluid, then gently brush over the warm apples to create a shiny glaze.
Allow to cool slightly before serving. Let the pastry rest for 5-10 minutes before cutting to allow the filling to set slightly. Serve warm with a scoop of vanilla ice cream or a dollop of whipped cream if desired.