In a saucepan, combine the potatoes and enough salted water to cover. Bring to a boil and simmer until tender, about 15 minutes. Drain, season with salt and pepper and mash; let cool.
Place 1/4 cup flour on a plate. Season the pork with salt and coat with flour. In a large skillet, heat 2 tablespoons oil over medium-high heat, add the pork and cook for 2 minutes on each side. Transfer to a work surface.
In the same skillet, over medium-high heat, add 1 tablespoon oil and the onion and cook, stirring, until softened. Stir in the remaining 2 tablespoons flour and cook for 1 minute. Stir in the chicken broth and olives and cook until thickened, about 2 minutes. Finely chop the pork, stir into the skillet and season with salt and pepper; let cool for 15 minutes.
In a large saucepan, heat the remaining oil to 350 degrees . Place the breadcrumbs on a plate, beat the eggs in a bowl and divide the potato into 4 portions. Shape each portion into a cup, fill with one-quarter of the pork mixture and shape the potato around the filling to form a ball. Coat with the breadcrumbs, turn in the egg and coat with more breadcrumbs.
Add the potato balls to the hot oil and cook, turning, until browned, 3 to 4 minutes. Drain on paper towels.