Place ribeye in the freezer for 1 hour. Remove from freezer, and thinly slice.
Whisk egg in a small bowl; set aside.
In medium sauté pan over medium heat, add olive oil and onion. Sauté onion until translucent and soft, 5-6 minutes.
Add ribeye and sauté until steak is slightly pink, about 5 minutes more. Sprinkle with salt and pepper. Add cheese and mix thoroughly until cheese begins to melt. Remove from heat, and strain in a fine mesh sieve if there is liquid in the pan. Let cool slightly.
Add oil to a medium Dutch oven, filling 3/4 of the way to the top. Preheat oil to 360°F.
Equally divide ribeye mixture in the centre of each egg roll wrapper. Fold wrapper in about 1/2 inch on each side. Brush egg roll wrappers with egg wash. Roll up and seal edges.
Place egg roll in oil, and fry for 3-4 minutes until golden brown, making sure to flip egg rolls while frying. Fry in batches to avoid over-crowding. Remove egg rolls to a paper-towel-lined plate. Serve hot.