Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat. Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet. Cook, breaking up the meat with a spoon, until browned and cooked through, about 7-8 minutes. Drain excess fat if necessary.
Stir in sliced mushrooms, diced green bell pepper, and sliced black olives. Cook for 5 minutes until vegetables are tender.
Add sliced beef or turkey pepperoni, pizza sauce, dried oregano, dried basil, crushed red pepper flakes, salt, and black pepper. Stir well to combine and cook for another 3 minutes. Remove from heat.
Roll out one pie crust and fit it into a 9-inch deep-dish pie pan, pressing it firmly against the bottom and sides.
Spread half of the shredded mozzarella cheese evenly over the crust.
Pour the beef and vegetable mixture over the cheese layer, spreading it evenly.
Sprinkle the remaining mozzarella and all of the provolone cheese evenly over the filling.
Cover the filling with the second pie crust. Trim any excess dough, then crimp the edges to seal the pot pie.
Cut several small slits in the top crust to allow steam to escape during baking.
Brush the top crust with the beaten egg to give it a golden, shiny finish.
Place the pie pan on a baking sheet to catch any drips and bake in the preheated oven for 40-45 minutes, or until the crust is golden brown and the filling is bubbly.
Remove from the oven and let cool for 10 minutes before slicing and serving.