Using a rolling pin, roll each slice of bread flat. Combine egg salad with the 2 tablespoons chives, oregano, or parsley. Spread about 2 level tablespoons of the egg salad over each bread square, covering to edges. Roll as tightly as possible. Cut each roll in half crosswise. Place rolls in layers in storage containers. Cover and chill up to 24 hours.
Just before serving, lightly spread mayonnaise or salad dressing on one end of each roll. Place parsley in a shallow dish. Dip spread ends of rolls in herb to lightly coat. Arrange on serving platters. Makes 96 appetizers.