Preheat the oven to 400ºF.
Spread out 8 squares of the puff pastry on baking sheets lined with parchment paper.
Layer slices of the pepperoni and salami in the center of each square, then top with a slice of the provolone.
Top each with the remaining squares of puff pastry and crimp the edges all around with a fork to seal.
Whisk together the egg with a couple tablespoons of water and brush each with the egg wash.
Bake for 15-20 minutes or until golden brown and bubbly.
Serve hot with warm pizza sauce on the side for dipping.