Boil the peeled and cubed potatoes in salted water for 15-18 minutes until fork-tender, then drain and mash until smooth with no lumps remaining.
Mix the mashed potatoes with flour, Parmesan, parsley, garlic powder, onion powder, salt, and pepper until a cohesive mixture forms that holds together when shaped.
Divide the potato mixture into 8 equal portions and shape each into oval or round patties about 1/2 inch thick, ensuring even thickness for uniform cooking.
Combine panko breadcrumbs with paprika and cayenne pepper in a shallow dish, spreading the mixture evenly for consistent coating.
Dip each potato patty into beaten eggs, coating completely, then press firmly into the panko mixture on both sides until fully covered.
Heat 1/4 inch of vegetable oil in a large skillet over medium-high heat until it reaches 350°F, testing with a breadcrumb that should sizzle immediately.
Fry the cutlets in batches for 3-4 minutes per side until deep golden brown and crispy, avoiding overcrowding the pan to maintain oil temperature.
Transfer the finished cutlets to a paper towel-lined plate to drain excess oil, then serve immediately while hot and crispy.