Begin by preparing the chicken: cut each thigh in half crosswise and place between two sheets of plastic wrap
Using a meat mallet or heavy pan, gently pound the chicken pieces to an even ¼-inch thickness
Pat the chicken dry with paper towels and season both sides with salt and pepper
Set up your breading station: in one shallow bowl, whisk together the eggs with the juice of one lemon
In another shallow bowl, combine the panko breadcrumbs, flour, Parmesan cheese, dried oregano, lemon zest, salt, and pepper
Dip each chicken piece first in the egg mixture, allowing excess to drip off, then press firmly into the breadcrumb mixture to coat completely
Place the breaded cutlets on a parchment-lined baking sheet and refrigerate for at least 15 minutes (or up to 4 hours) to help the coating adhere
While the chicken rests, prepare the herb sauce: combine the lemon zest, lemon juice, parsley, oregano, salt, and pepper in a food processor or blender
Pulse several times to roughly chop the herbs, then slowly drizzle in the olive oil while pulsing until the sauce is well combined but still has texture
Transfer the sauce to a bowl and set aside at room temperature to allow flavors to develop
When ready to cook, heat a large skillet over medium heat and add 2 tablespoons each of olive oil and butter
Once the butter is melted and bubbling, add half of the chicken cutlets to the pan, being careful not to overcrowd
Cook until golden brown and crispy, about 2-3 minutes per side, adjusting heat as needed
Transfer the cooked cutlets to a paper towel-lined plate and repeat with remaining oil, butter, and chicken
Just before serving, add the minced garlic to the still-warm skillet and cook for 30 seconds until fragrant
Stir the garlic into the herb sauce and spoon generously over the crispy chicken cutlets