If the chicken breasts are thick, slice each one horizontally into two thinner cutlets, as shown in your process photos.

Season the chicken with the salt and black pepper.

On a shallow plate, combine the flour, finely grated Parmesan, and garlic powder.

Coat each chicken piece lightly in the flour mixture and shake off the excess.

Heat the olive oil and 1 tablespoon salted butter in a large skillet.

Add the chicken and cook until golden on both sides and the center reaches 165°F (74°C). Work in batches if necessary.

Transfer the cooked chicken to a clean plate.

Add the sliced garlic to the skillet and cook briefly until fragrant without letting it burn.

Pour in the white wine and scrape up the browned bits from the bottom of the skillet.

Let the wine reduce slightly.

Add the chicken broth, lemon juice, and drained capers.

Simmer until the sauce reduces slightly and the flavors come together.

Return the chicken to the skillet and spoon the sauce over the top.

Lower the heat and swirl in the 2 tablespoons cold salted butter until the sauce looks glossy.

Finish with fresh parsley and serve with lemon wedges if desired.