Lay a piece of plastic wrap on a work surface, place a chicken breast half on top and lay another piece of plastic wrap on top of that. Pound the chicken breast with a rolling pin or the bottom of a heavy skillet until it is about ¼ inch thick. Repeat with remaining chicken breasts.
Put almonds in food processor and process in pulses until the almonds turn into a fine meal. Be careful not to turn it into paste. Add the Parmesan cheese, salt and pepper and pulse a couple more times to mix. If using almond meal, just mix the flour, cheese, salt and pepper together. Spread the mixture on a large plate.
Rinse the pounded chicken breasts in water and shake off the excess. Dredge the chicken in the almond mixture, gently pressing the mixture onto the chicken.
Heat a large skillet over medium high heat. Add the olive oil and 2 tablespoons of butter. Once the oil is hot and the butter melted, place two prepared chicken breasts in the pan – do not over crowd! Cook for 3 -4 minutes or until they are well browned. Flip and cook for 3- 4 minutes on the other side. Remove cooked chicken breasts to a serving dish and cover with foil to keep warm. You can also place the plate in a warm oven. Repeat procedure with the remaining chicken breasts.
Add the wine or chicken stock and lemon juice to the pan. Scrape the pan to incorporate all the browned bits of almond. Add the capers and cook until the sauce is reduced by about half. It should be the consistency of light syrup. Stir in the remaining butter until melted.
Pour the sauce over the chicken breasts, top with chopped parsley and serve with lemon slices or wedges.