Line a baking sheet with parchment.

Heat 1 tablespoon of olive oil in a large cast-iron skillet over medium-high heat; add the onions and cook until softened and slightly browned, about 20 minutes.

Stir in the oregano, garlic and red and yellow peppers and cook for another 5 minutes.

Set aside to cool for 20 minutes.

Heat the remaining 1 tablespoon olive oil in another large cast-iron skillet over medium-high heat.

Add the sausage and cook, using the back of a wooden spoon to break up the sausage meat into small bits, until browned, 10 to 15 minutes.

Set aside to cool for 20 minutes.

On a lightly floured surface, roll out each puff pastry sheet to about 13 inches long and 10 inches wide.

Place one of the puff pastry pieces on the lined baking sheet; set aside the other piece.

Whisk the egg in a small bowl with 1 tablespoon water.

Sprinkle 2 cups of the Monterey Jack cheese over the puff pastry sheet on the baking sheet, leaving a 1/2-inch border around the edges of the pastry.

Continue layering with half the caramelized onions and peppers, sausage and pepperoni; finish with half the mozzarella slices.

Brush the border of the puff pastry with the egg wash, lay the remaining puff pastry pieces over top and use a fork to crimp the edges.

Using a sharp paring knife, cut three 1 1/2-inch vents in the top.

Put the pie into the fridge to chill for 30 minutes before cooking.

Preheat the oven to 425 degrees F

Brush the pie with the egg wash.

Bake on the bottom rack until the pastry is nicely browned, about 20 minutes.