Set up a dredging station with three shallow bowls: flour in the first; beaten eggs in the second; and a mixture of Panko, Parmesan, oregano, salt, and pepper in the third.
Dredge each chicken cutlet in the flour, shaking off any excess.
Submerge the floured chicken into the egg wash, allowing any excess to drip off.
Press the chicken firmly into the Panko-Parmesan mixture on both sides until evenly coated.
In a large skillet, heat olive oil and butter over medium-high heat until the butter is melted and foaming.
Working in batches, place the cutlets in the skillet and fry for 3 to 4 minutes per side until the breading is golden brown and the internal temperature reaches 165°F (74°C).
Transfer the cutlets to a wire rack or paper-towel-lined plate to drain briefly.
Serve immediately garnished with fresh parsley and lemon wedges for squeezing over the top.