In a large skillet over medium heat, cook the shaved steak until browned and cooked through, about 5 minutes. If the beef has enough fat, you will not need any, but if it sticks, give it a quick coating of cooking spray. Season the beef with salt and pepper. As it is cooking, using tongs separate the larger pieces.
Add the onion and green pepper, cook stirring occasionally for about 5 additional minutes until they are softened.
Remove the meat mixture from the heat and place into a larger mixing bowl. Allow the beef to cool for at least 10 minutes.
Stir in the mozzarella cheese and mix well. Allow this filling to sit another 10 minutes to cool.
On a clean cutting board or workspace, place an egg roll wrapper in the center with the points facing up/down.
Using your fingers or a pastry brush, add a small amount of water on the top edges of the wrapper.
Place about 2 ounces (about 2 tablespoons) of the meat filing into the lower center of the egg roll.
Bring the bottom egg roll wrapper point up over the filling, bring the left corner into the center (covering the first wrapper fold), then the right side corner to the center (the roll should look like an envelope). Roll up onto the final corner, tightening and forming the roll a bit before finally sealed.
Set each roll aside on a parchment lined tray and continue rolling the rest of the egg rolls.
Heat the cooking oil in a larger Dutch oven or frying skillet to 325°F.
Using a metal spoon, metal tipped tongs or a spider spoon, gently lower one egg roll at a time into the oil. I would not recommend making more than 4 at a time. If you pan is smaller, fry 2-3 at a time making sure to not crowd the food. Fry until golden brown, about 90 seconds to 2 minutes.
Remove from the oil to a wire rack over a paper towel lined tray or plate to drain. Repeat with the remaining egg rolls.
Garnish with fresh chopped parsley and serve with ranch, cheese whiz or queso sauce for dipping, optional.
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Notes
Make Ahead- Egg rolls can be made up to 1 day ahead of time and refrigerated until ready to fry.
Freezing- After assembling egg rolls, place into a container separated by parchment or wax paper and freeze for up to 6 months. Fry from a frozen state, adding 2 more minutes to the cook time.