In a large skillet over medium-high heat, cook the ground beef and diced onions until the beef is fully browned and the onions are translucent.
Drain excess fat from the skillet and return to heat.
Stir in salt, black pepper, and Worcestershire sauce, then remove from heat and allow to cool slightly.
Fold in the shredded cheddar cheese and chopped pickles until evenly distributed.
Lay an eggroll wrapper on a clean surface in a diamond orientation and place 2-3 tablespoons of the beef mixture in the center.
Brush the top edges of the wrapper with the beaten egg wash.
Fold the bottom corner over the filling, tuck in the side corners, and roll tightly toward the top corner to seal.
Heat the vegetable oil in a deep pot or fryer to 350°F (175°C).
Fry the eggrolls in batches for 3 to 5 minutes, turning occasionally, until the exterior is golden brown and crispy.
Drain on a wire rack or paper towels and serve warm with dipping sauce.