Cook and stir half of the shaved steak in a large skillet over medium heat until browned, 3 to 5 minutes. Transfer to a plate. Repeat with remaining steak. Drain juices from the steak; cut into small pieces.
Combine steak, American cheese, green bell pepper, red bell pepper, and yellow bell pepper in a bowl. Season with salt and pepper.
Lay 1 egg roll wrapper on a flat surface in the shape of a diamond. Place a large spoonful of the steak mixture in the center. Fold the bottom corner and opposing sides over the steak mixture; roll up wrapper towards the top corner. Repeat with remaining egg roll wrappers and steak mixture.
Heat oil in a deep-fryer or large saucepan. Place a few egg rolls in the hot oil, seam-side down. Fry, turning occasionally, until golden brown, 2 to 3 minutes. Repeat with remaining rolls.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. Amount will vary depending on cooking time and temperature, ingredient density, and specific type of oil used.