Cook beef in a large skillet over medium heat, gently breaking it into pea-sized pieces, until browned, 5 to 7 minutes. Gently stir in Worcestershire sauce, salt, and pepper, then transfer mixture to a bowl.

Melt butter in the same skillet over medium heat. Add onion and bell pepper; cook and stir until translucent, 5 to 7 minutes. Return beef mixture to the skillet and stir to combine. Remove from the heat and let cool slightly, about 10 minutes.

Lay egg roll wrappers on a flat surface. Place 1/2 slice American cheese onto each wrapper, then top with about 3 tablespoons filling. Pull the bottom left corner up over the filling and fold the two sides in, moistening the edges with water as you go; roll tightly.

Fill a large saucepan with about 1 inch oil; heat over medium-high heat. Working in batches of 3 to 4, fry egg rolls until browned on all sides, 3 to 4 minutes. Drain on a paper towel-lined plate.