Preheat the oven and prep the baking sheet: Preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper and set aside.
Trim and wash the asparagus: Trim the ends of asparagus by simply bending the spears at the cut end and the tough part will snap off where the lignin has stopped forming. Wash trimmed asparagus in a colander and dry.
Season the asparagus: In a bowl, toss together the asparagus, olive oil, salt and pepper.
Roll and cut the pastry: Roll the two pastry sheets out on a floured surface and cut each sheet into 4 equal squares, 8 squares total between the 2 sheets.
Add the Brie: Place a slice of Brie Cheese right in the middle of each square, leaving space around the edges to make a parcel.
Layer the asparagus and Gruyere: Then add 8 to 10 asparagus spears on top of the piece of brie cheese and top each bundle with the gruyere cheese.
Wrap and transfer to baking sheet: Take 2 corners of the pastry and wrap up and over the asparagus to enclose. Transfer to the prepared baking sheet. Repeat with remaining squares.
Brush and garnish: Brush each pastry with egg and sprinkle the dough with flaked almonds (about 1 tablespoon per bundle).
Bake until golden: Transfer to the oven and bake for 20–25 minutes or until golden brown.
Make the honey butter: Meanwhile, melt together the honey and butter in the microwave for approx 2 minutes until butter is melted and the honey and butter are combined. Stir together and let sit to cool until the Asparagus Puff Pastry is ready to be served.
Serve and drizzle with honey butter: Serve the pastries warm, re-whisk the honey butter mixture and drizzle lightly over the asparagus puff pastry bundles.