Step 1: Cook the Beef: Heat a large skillet over medium heat. Cook the 1 pound ground beef, breaking it apart as little as possible so that the meat is still in pea-sized chunks, until browned (5 to 7 minutes). Drain any excess grease. Add the 1 tablespoon Worcestershire sauce, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Stir gently and remove the mixture from the pan.
Step 2: Sauté Vegetables: Melt the 2 tablespoons butter in the same skillet. Add the chopped yellow onion and 1/2 chopped green bell pepper; cook and stir until they are softened and lightly browned (5 to 7 minutes). Return the beef mixture to the skillet and stir to combine. Let the filling cool slightly while preparing the wrappers.
Step 3: Assemble the Egg Rolls: Lay the 24 egg roll wrappers on a flat surface. Place 1/2 a slice of American cheese onto the center of each wrapper. Add about 3 tablespoons of the beef filling on top of the cheese. Pull the bottom corner up over the filling, fold the two side corners in, moistening the edges with water as you go, and roll tightly toward the remaining corner to seal.
Step 4: Fry: Heat about 1 inch of vegetable oil in a large saucepan or deep skillet over medium-high heat. Add 3 to 4 egg rolls at a time (do not overcrowd the pan) and fry until browned and crispy, about 3 to 4 minutes, flipping halfway. Repeat with the remaining egg rolls, allowing the oil to come back up to temperature between batches.2
Step 5: Serve: Serve warm with ketchup or cheese sauce.