Place the pork fillets between two sheets of plastic wrap, and pound them with a meat mallet to at least ¼-inch thick.
Remove the plastic wrap and place the pork in a small bowl. Add the garlic, lemon juice, parsley, and salt and marinate in the fridge for 1-2 hours.
Remove the pork from the fridge and lay the fillets flat. Cover the fillets with a thin layer of the jamón serrano, and then place the sticks of cheese end-to-end along one of the long sides of each pork fillet.
Carefully roll the pork and ham into a log around the cheese sticks, so that the pork forms the outer layer of a log. Roll each log in flour, then in the beaten egg, and then in the breadcrumbs.
Meanwhile, place a large heavy skillet over medium-high heat and fill with olive oil to a depth of ¼-inch and heat to 350°F (177°C).
When the oil is heated, fry the flamenquínes one at a time, placing them open side down in the pan. Cook each side until golden to ensure that the pork is cooked through and the cheese is gooey. Drain the flamenquínes on a paper towel to drain any excess oil.
Serve hot with a garden salad, french fries, and/or alioli for dipping.