Cut each chicken breast in half vertically. This will leave you with 2 pieces – one will be thinner, which is already a perfect cutlet size. Take the thicker piece and cut it in half horizontally into 2 thinner pieces. You should have 3 pieces altogether.
Place the chicken pieces on a cutting board and cover them with a piece of plastic wrap or parchment paper. Using a meat tenderizer, pound the chicken until it’s ½ cm or ¼ inch thickness.
Drizzle the cutlets with oil and season with salt and pepper.
Combine flour, parmesan, salt, and pepper in a shallow bowl and place each piece of chicken into the flour, turn to coat and then shake off any excess.
Heat the remaining olive oil and 1 tablespoon of butter in the skillet over medium-high heat and cook the chicken for 3-4 minutes and then flip over and continue cooking until golden brown. Cook in batches and do not overcrowd the pan. Remove the cutlets from the skillet onto a plate.
Add wine (or chicken stock) to the skillet and cook until it reduces in half. While the wine is simmering, scrape off any brown bits stuck to the bottom of the skillet with a wooden spoon. They add lots of flavor! Add lemon, garlic, and remaining butter and cook gently until the sauce emulsifies.
Add in the capers and parsley and stir before removing from the heat. Season your chicken piccata to taste.