Combine mashed potatoes, pork, grated apple, onion, sage and bread crumbs, if using, in a large bowl. Work with your hands to thoroughly mix ingredients. Season with salt and pepper.
Working on a lightly floured surface, divide the pork mixture into eight equal portions and form round cakes. Cover and refrigerate for 15 minutes or longer, until you're ready to cook them.
Heat 2 tablespoons of olive oil each in two large nonstick skillets over medium-low flame (or use one skillet and cook cakes in two batches, holding cooked cakes in warm oven). Add 4 cakes to each skillet and cook for about 7 minutes undisturbed.
Very carefully flip cakes (infuriatingly, they become more fragile as they cook, not less so). Cook 7 to 8 minutes, until cooked through.
Meanwhile, heat 1 tablespoon of olive oil in a medium nonstick skillet over medium flame. Add apple slices and toss to coat with oil. Season with salt and pepper and cook for about 5 minutes, stirring occasionally.
Very carefully transfer two cakes each to serving plates. Divide sautéed apples among plates and serve.