Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
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.
In a bowl toss together the asparagus, olive oil, salt and pepper.
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.
Place a slice of Brie Cheese right in the middle of each square, leaving space around the edges to make a parcel.
Then add 8 to 10 asparagus spears on top of the piece of brie cheese and top each bundle with the gruyere cheese.
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 each pastry with egg and sprinkle the dough with flaked almonds (about 1 tablespoon per bundle).
Transfer to the oven and bake for 20-25 minutes or until golden brown.
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 the pastries warm, re-whisk the honey butter mixture and drizzle lightly over the asparagus puff pastry bundles.