Prepare the chicken. Slice the chicken breasts lengthwise into 4–6 thinner pieces. Place between plastic wrap and pound to about ¼-inch thickness.
Make the dredge. In a shallow bowl, mix the flour, salt and pepper, Parmesan, oregano, and garlic powder.
Dredge the chicken. Coat each chicken cutlet in the seasoned flour, shaking off any excess.
Sear. Heat a large skillet over medium heat and add olive oil. Cook the chicken in batches for about 3–4 minutes per side, until golden and cooked through. Transfer to a plate and set aside.
Build the sauce. In the same skillet, add more oil if needed and sauté the garlic for 30–60 seconds until fragrant.
Deglaze. Pour in the white wine and chicken stock, scraping up any browned bits from the bottom of the pan. Simmer for 2–3 minutes to reduce slightly.
Add lemon. Stir in the lemon juice and sliced lemons. Let the sauce simmer another 2–3 minutes.
Finish the sauce. Reduce heat to low and whisk in 2–4 tablespoons butter until glossy. Stir in capers and chopped parsley. Taste and adjust seasoning.
Finish the dish. Return the chicken to the pan and spoon the sauce over the cutlets. Alternatively, place the chicken on a platter and pour the sauce over the top.