Boil, peel and then slice eggs in half lengthwise. Scoop out the yolks and discard. Set the hard-boiled egg halves aside.
In a small saucepan, cook the raw egg whites over medium heat until cooked through. In a food processor or blender, puree the egg whites, lime juice and avocado thoroughly.
Add black pepper and red onion to egg-avocado puree. Spoon mixture evenly into hard-boiled egg halves and sprinkle paprika on top. Chill for at least 1 hour. Serve chilled.