Add broth, oregano, and garlic powder to a small pot and bring to a boil.
Chop meat roughly and add to the broth. Reduce heat to a simmer while you prep everything else.
Make sure your puff pastry is thawed and unfold it.
If you want, you can pinch the seams where the puff pastry was folded and roll it all with a rolling pin.
Cut the puff pastry sheet into four equal squares.
Scoop out about 3 tablespoons of meat from the pot with the meat and broth and place it in the center of two of the squares. Do not discard any leftover broth.
Top the meat with a tablespoon or so of giardiniera.
Whisk an egg with a tablespoon of water to make an egg wash. Using your fingers or a brush, spread the egg wash liberally around the edges of the squares holding the meat/giardiniera. This egg wash will help the two pieces of puff pastry stick together.
Place the bottom squares on top of the meat/giardiniera. Using a fork, press the edges of the two pieces of puff pastry together and make sure to poke some holes with the fork at the very top of the sealed pastry. The holes on the top will let steam out so that hopefully you will not have any explosions in the oven
Transfer over each puff pastry pocket to a parchment-lined sheet pan or cookie pan. You might need a knife or spatula to lift these up and move them easily. Alternatively, do all of this on the parchment so you can move it easily.
Bake at 375 degrees F (190 C) for 25 to 30 minutes.
Serve and enjoy. Serve any leftover broth on the side for dipping.