Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper and roll out the puff pastry sheet on a lightly floured surface to form an even rectangle. Transfer the pastry to the prepared baking sheet.
Slightly toast the sliced almonds in a dry skillet over medium heat until golden brown and fragrant, about 3-4 minutes. Remove from heat and set aside.
Trim the woody ends off the asparagus and slice the stalks into very thin, lengthwise ribbons using a sharp knife or mandoline. Arrange these asparagus slices evenly over the puff pastry, leaving a small border around the edges.
1 sheet Puff pastry sheet
Drizzle the asparagus and pastry with olive oil, then season with a pinch of salt and black pepper. Brush the exposed edges of the puff pastry with the beaten egg wash for a shiny, golden finish.
1 sheet Puff pastry sheet
Bake in the preheated oven until the pastry is puffed and golden, about 20-25 minutes. The asparagus should look tender and slightly crisp at the edges, and the pastry should have a flaky, golden crust.
Once baked, sprinkle the toasted almonds evenly over the top of the tart. Slice into squares and serve immediately, enjoying the crisp pastry with tender asparagus and nutty almond topping.
1 sheet Puff pastry sheet