Step 1: Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
Step 2: On a lightly floured surface, roll out the puff pastry sheet slightly larger than your desired tart size, approximately 10x14 inches. Trim the edges to create a neat rectangle or circle. Transfer the pastry to the prepared baking sheet. Score a border about 1/2 inch from the edge of the pastry, being careful not to cut all the way through.
Step 3: Prepare the apples. Using a very sharp knife or a mandoline, slice the apples as thinly and uniformly as possible (about 1/16 inch thick). Immediately toss the apple slices with lemon juice in a bowl to prevent browning.
Step 4: In a small bowl, combine 1/4 cup granulated sugar and ground cinnamon.
Step 5: Begin arranging the apple slices on the puff pastry, working within the scored border. Overlap the slices slightly in rows, circles, or a mosaic pattern to create your geometric design. Be mindful of maintaining even thickness and spacing for the best visual effect.
Step 6: Once all apples are arranged, brush the melted butter generously over the apple slices. Sprinkle the cinnamon sugar mixture evenly over the apples.
Step 7: If using, brush the scored edges of the puff pastry with the egg wash for a golden finish.
Step 8: Bake for 25-30 minutes, or until the pastry is golden brown and puffed, and the apples are tender. Keep an eye on the tart; if the edges brown too quickly, you can loosely tent it with foil.
Step 9: Remove from oven and let cool slightly on the baking sheet before transferring to a wire rack to cool completely. Serve warm or at room temperature.