In a medium bowl, whisk together eggs, Worcestershire sauce and Tabasco. Season with salt and pepper. Pour mixture into a wide, shallow dish.
Layer 2 slices bread with equal amounts of the sliced ham and cheese; top with remaining bread slices to make sandwiches and press down to secure filling. Dip sandwiches into egg mixture and turn to coat both sides.
Heat the oil in a frying pan over medium heat. Cook sandwiches 3 minutes on each side, or until golden brown and cheese has melted. Serve hot.