2. Slice the unpeeled potatoes about 1/16" thick and lay them in an overlapping "fish scale" pattern on the surface of the fillets.
3. Coat a 10" skillet or sauté pan with oil and heat over medium-high heat. Gently lift each fillet by sliding one hand underneath the waxed paper and carefully flipping the fillet over into the pan (potato side down), being careful not to splash the hot oil. Add more oil to the pan so that the potato "scales" are immersed. Cook for 3 minutes, or until the edges of the potatoes begin to turn golden brown. Using a perforated spatula, gently turn the fillets over and cook 1 minute more.
To Serve: Remove the fillets from the pan and place on warm serving plates. Sprinkle with the parsley and garnish with the lemon wedges. Serve immediately.