Place the pork fillets between two sheets of plastic wrap, and use a meat mallet to flatten to ¼-inch thick at most.
Remove the plastic wrap and place the pork in a small bowl. Add the garlic, lemon juice, parsley, and salt and leave to marinate in the fridge for 1-2 hours.
Remove from the fridge and lay the pork out flat. Cover completely with a thin layer of the jamon 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.
When the oil is heated, fry the flamenquines one by one, 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. Remove the flamenquines from the pan and place on a paper towel to drain any excess oil, and serve hot with a garden salad and/or french fries.