Slice the abalone into 1/4 inch thick steaks, making sure to trim off any meat that is not white, as this part tends to be very tough. Place the steaks on a cutting board, and pound with a meat tenderizer until pliable.

In a small bowl, stir together the ketchup, horseradish, and lime juice to make a cocktail sauce. Refrigerate until ready to use.

Heat olive oil in a large heavy skillet over medium heat for about 5 minutes. Whisk eggs and milk together in a shallow dish. Place bread crumbs in a large resealable plastic bag. Dip the abalone steaks in egg, then place in the bag with the crumbs and shake to coat.

Fry coated abalone for 3 to 5 minutes on each side, until golden brown. Remove to paper towels to drain. Place on a platter, and garnish with lime slices and parsley. Serve with the cocktail sauce for dipping.