Remove puff pastry. Preheat the oven to 375°F.
Wash and trim the asparagus.
Melt butter in the microwave. In a bowl, mix asparagus, butter, olive oil, salt and pepper until asparagus is well coated.
Crack open the egg, and lightly beat with a fork.
Roll out puff pastry and cut into 8 equal pieces.
To each square, add a slice of brie, then a piece of prosciutto, then 4 stalks of asparagus. Fold the first corner over the asparagus bundle then brush the opposite corner with an egg wash. Fold that over the first corner and press to close. Repeat the process until all are done. Please each one on a piece of parchment paper on a baking tray.
Egg wash the top of each bundle, and then sprinkle with Everything but the Bagel seasoning.
Bake for 20-25 minutes, or until puffy and golden brown colored. Allow to cool for a few minutes and serve.