Heat a skillet over medium heat. Cook beef, breaking apart as little as possible, until browned and still the size of peas, 5 to 7 minutes. Add Worcestershire sauce, salt, and pepper. Stir gently and remove mixture from pan.Advertisement
Melt butter in the skillet. Add onion and bell pepper; cook and stir until browned, 5 to 7 minutes. Return beef mixture to the skillet and stir to combine. Let filling cool while preparing the wrappers.
Lay egg roll wrappers on a flat surface. Place 1/2 a slice of American cheese onto each. Add 3 tablespoons of the filling on top of each egg roll. Pull the bottom left corner over the filling and fold the two sides in, moistening edges with water as you go; roll tightly.
Heat about 1 inch oil in a large saucepan over medium-high heat. Add 3 to 4 egg rolls at a time and fry until browned, 3 to 4 minutes. Repeat with remaining egg rolls.