Cook the Potatoes: Boil or steam the potatoes until fork-tender. Drain well and let them cool slightly.
Prepare the Filling: While the potatoes are cooking, brown the ground beef in a skillet. Add the onions and garlic and cook until softened. Stir in cumin, paprika, salt, and pepper. Add optional ingredients like olives, raisins, or hard-boiled eggs. Make sure the filling is not too wet.
Mash the Potatoes: Mash the cooked potatoes until smooth. Mix in 1-2 eggs, flour, and salt. The mixture should resemble playdough – moldable but not sticky.
Shape the Rellenos: Take about 1/2 cup of the potato mixture and flatten it into a disc in your palm. Make a well in the center. Spoon 2 tablespoons of picadillo into the well. Gently bring the edges of the potato disc together to enclose the filling, pinching to seal. Shape into an oval or football shape.
Breading: Roll the relleno in flour, then dip it in beaten egg, and finally, coat it generously with breadcrumbs.
Fry the Rellenos: Heat oil in a deep pot or skillet to 350-375°F (175-190°C). Carefully place the rellenos in the hot oil and fry for 3-5 minutes per side, until golden brown and crispy. Do not overcrowd the pan.
Drain and Serve: Remove cooked rellenos with a slotted spoon and place them on a wire rack or paper towel-lined plate to drain excess oil. Serve hot with optional garnishes like salsa criolla or aji amarillo sauce.