Preheat the oven to 175 degrees Celsius/ 350 degrees Fahrenheit. Line a baking sheet with baking paper.
Cut each chicken breast horizontally to obtain two large, thinner pieces. Next, cut these slices in two vertically so that you have 4 pieces of schnitzel from 1 chicken breast; each piece should weigh approximately 50 g/ 1.7 oz.
Tenderize: If the chicken breasts are smaller, cut them only once horizontally and tenderize gently. Place each chicken piece between two sheets of plastic foil and tenderize slightly using a meat mallet or a heavy saucepan. Sprinkle the chicken generously with salt and pepper.
Prepare potatoes: Clean and peel the potatoes. Grate them roughly using the large side of a box grated directly onto a clean kitchen towel. Form a bundle with the kitchen towel and squeeze the potatoes very well, trying to release as much liquid as possible from the potatoes.
Combine: Place the squeezed potatoes in a large casserole dish. Add the Parmesan and the dried breadcrumbs. Mix very well.
Place the flour on a plate and whisk the eggs lightly in a shallow bowl.
Coat the chicken pieces in flour, shake to remove the excess, dip them in the eggs, and coat with the potato-Parmesan mixture. Press lightly to ensure that the coating is holding its place.
Fry: Heat a large heavy cast-iron skillet or a thick-bottomed non-stick pan. Add two tablespoons of the oil. When the oil is hot, add the first batch of schnitzel and fry them for about 2-3 minutes on each side until the coating is golden. Place the fried chicken on the baking tray and continue with the second and maybe third batch. Add 1 or 2 tablespoons of oil for each new batch of chicken breast.
Batches: After each batch, remove the potatoes pieces that might remain in the skillet with a spatula; if you leave them there until all the frying is done, they will burn and stick to the other chicken pieces.
Bake: When all the pieces are on the baking tray, place them in the oven and bake for about 6-8 minutes or until cooked through.