Pat the cutlets very dry with paper towels. Season both sides with salt and pepper. If any pieces are uneven, pound them gently to about 1/4 inch thickness.

Set up a dredging station: bowl of flour, bowl of beaten eggs, and a bowl with breadcrumbs mixed with 1/2 cup grated Parmesan.

Coat a cutlet lightly in flour, shaking off the excess. Dip it into the egg, then press it firmly into the breadcrumb-Parmesan mixture so the crumbs adhere well. Repeat with the remaining cutlets.

Heat the olive oil in a large skillet over medium-high until it shimmers. Add the cutlets without crowding the pan. Cook 3 to 4 minutes per side until golden brown and crusty. Transfer to a plate and tent loosely with foil to keep warm.

Reduce heat to medium and add the butter to the same skillet. When it melts, add the minced garlic and sauté for about 30 seconds until fragrant but not browned.

Pour in the chicken broth and scrape the bottom of the pan to lift the browned bits. Stir in the heavy cream and the remaining 1/4 cup Parmesan. Simmer gently until the sauce thickens, about 3 to 4 minutes. Taste and season with salt and pepper.

Return the cutlets to the skillet and spoon sauce over them. Warm together for about a minute so the chicken soaks up some sauce. Garnish with chopped parsley or thyme and serve immediately.