To begin, boil peeled potatoes in salted water until very soft, about 20 minutes. Drain thoroughly and mash while still hot. Let cool slightly, then mix in one egg and a pinch of salt until smooth. Set aside and allow to cool fully before shaping.
Heat oil in a frying pan over medium heat. Add chopped onion and sauté until translucent. Stir in garlic, cumin, paprika and tomato paste. Cook briefly before adding the beef. Continue until browned, then season and mix in olives, chopped egg, and parsley. Let the filling cool before use.
With wet hands, take a handful of cooled mashed potato and flatten it into a patty. Spoon 1–2 tbsp of the beef filling into the centre. Gently fold the edges around to seal and shape into a slightly oval form. Repeat until all the filling and mash are used.
Lightly dust each filled potato with flour. Then dip into the beaten egg to coat completely. This forms a crisp golden crust when fried. Transition to heating your oil.
In a deep skillet, heat oil over medium heat. Carefully place each potato into the oil and fry until golden brown on all sides, turning gently as needed. Do not overcrowd the pan. Continue to draining.
Remove fried Papa Rellena and place on kitchen paper to absorb excess oil. Let rest for 2–3 minutes before serving. Meanwhile, prepare garnishes.
Arrange the hot Papa Rellena on a plate with salsa criolla or ají sauce. Garnish with lime wedges or fresh herbs if desired. Best enjoyed while crisp and warm for full flavour and texture.