Heat 1 tablespoon vegetable oil in a large skillet over medium heat. Cook and stir onion in hot oil until onion is translucent, about 5 minutes. Break frozen steak pieces into the skillet; cook and stir until steak is no longer pink, about 10 minutes. Remove from heat and set aside.

Arrange 8 egg roll wrappers on a flat surface; place a half cheese slice on each one. Layer an equal amount of steak-onion mixture on top of each cheese slice. Roll up wrappers according to package directions and seal edges, wetting with water if necessary.

Heat 1 inch oil in a deep fryer or large skillet to 375°F (190°C). Working in batches, fry egg rolls in hot oil until golden brown on all sides, about 5 minutes. Remove; drain on paper towels.