Cut potatoes into thick fry-style sticks and soak in cold water for at least 30 minutes; drain and pat completely dry.
Toss the potatoes with olive oil, paprika, salt, and black pepper.
Oven method: Bake at 425°F (220°C) for 35–40 minutes, flipping halfway, until crisp.
Air fryer method: Air fry at 380°F (193°C) for 15–18 minutes, shaking every 5 minutes.
Deep-fry method: Fry at 350°F (175°C) for 7–8 minutes, rest 10 minutes, then fry again at 375°F (190°C) for 2–3 minutes.
While fries are hot, toss with minced garlic, lemon juice, oregano, and a drizzle of olive oil.
Top with feta, garnish with parsley, and serve with lemon wedges.