Slice the ribeye into thin strips.
1 pound beef ribeye
Add the olive oil to a large skillet and add the peppers, onions and mushrooms to the pan. Saute for about 8 minutes over medium-high heat. The veggies should be soft and browned.
2 Tablespoons olive oil, 2 green bell peppers, sliced, 1 yellow onion, sliced, ½ pound sliced mushrooms
Remove the veggies from the skillet and set aside in a bowl.
Add the sliced beef to the same skillet and saute for another 8 minutes, tossing occasionally, to fully cook the beef. There should be no pink on the meat and it should be completely browned.
Add the veggies back into the skillet and toss with the beef then remove the skillet from the stovetop. Add the slices of cheese and stir. The cheese will melt from the heat of the beef and veggies.
½ pound sliced provolone cheese, 1 ½ teaspoon salt, ½ teaspoon ground black pepper
Pour any excess juice in the skillet off and discard. You don’t want the filling to be too wet.
Let the filling cool for about 10 minutes.
Fill a deep skillet with about 4 cups of canola oil. You want to have at least 3 inches of oil in the pan. Heat the oil over medium heat.
Canola oil for frying
While the oil is heating, assemble the egg rolls.
Lay the 8 egg roll wrappers on a clean work surface and divided the filling mix between the wrappers, putting it in the middle of each wrapper.
8 egg roll wrappers
Whisk the egg and milk together in a small both then brush around the edges of the egg roll wrappers with a little bit of the egg wash mix. This will help the egg rolls seal as they fry.
1 egg, 1 Tablespoon whole milk
To roll the egg roll, fold the sides of the wrapper inward and then fold the bottom of the wrapper up, covering the filling. Roll the wrapper upward to make the egg roll.
Submerge the egg rolls in the hot oil and fry. Cook only about 3-4 egg rolls at a time to prevent over crowding in the pan. Fry for about 3 minutes, flip (if needed) and cook for another 2 minutes. The egg rolls should be golden brown.
Serve while hot.