Heat (1) tablespoon oil in a large pan over medium high heat. Add the onions, red and green peppers, season with salt and black pepper to taste, and sauté until softened, about 4-5 minutes.
Drizzle in the remaining (1 tablespoon) oil into the pan and add in the shaved beef. Use a large spoon to help breakup the meat. Mix in the garlic powder, onion powder, salt and black pepper and Worcestershire sauce. Cook mixture until the meat is fully cooked and any released liquid is mostly absorbed. Mix in (1) cup of mozzarella cheese. Once all the cheese is melted and incorporated into meat filling, remove pan from heat. Set pan aside to let the meat filling cool to room temperature.
In a small dish, whisk together the egg and water. Set aside. On a clean surface, place down (2) sheets of egg roll wrapper. Top with a slice of provolone cheese and add about (1 to 1 1/2 tablespoons) of mozzarella cheese. Spoon over a portion of the cooked meat filling. Top with another (1 to 1 1/2 tablespoons) of mozzarella cheese.
Using a pastry brush, apply some of the egg wash over the outer edges of the egg roll wrapper. Fold the bottom and side edges of the wrapper over the filling and roll the wrapper onto itself to enclose. Repeat with remaining filling, wrappers and cheese for a total of (8) egg rolls.
Heat up of oil (about 3 to 4 cups) in a large heavy bottom pot to 350F. In batches, fry the egg rolls until golden brown, 3-4 minutes per side or longer as needed. Transfer to a wire rack placed over a paper towel lined baking sheet to catch any excess oil.
Serve egg rolls immediately while still hot on its own or with sauce of choice. Enjoy!