1. Slice eggs in half lengthwise, and carefully remove yolks, keeping egg whites intact.
2. Grate egg yolks using small holes of a box grater. Mash together yolks, mayonnaise, and next 3 ingredients. Add hot sauce, if desired.
3. Mash together avocados and lime juice. Stir avocado mixture and tarragon into yolk mixture. Add salt and pepper to taste.
4. Spoon or pipe yolk mixture into egg white halves. Top with desired amount of parsley leaves.