Place a slice of prosciutto on top of each pounded cutlet. Place one sage leaf in the middle of the prosciutto slice. Use a toothpick to gently thread the prosciutto and sage to the chicken (see video for reference).

Place the flour onto a platter or large plate. Stir in ½ tsp black pepper into the flour (no need to add salt, the prosciutto is salty enough). Dredge each cutlet through the flour until fully coated. Shake off any excess flour. Set aside.

Heat the oil in a large skillet over medium-high until shimmering. Place the cutlets into the oil, prosciutto-side down, carefully nudging them around in the oil a bit to keep them from sticking to the skillet. After 2 to 3 minutes, the prosciutto should be getting crispy. Flip the cutlets over and cook for another 2 to 3 minutes, nudging the cutlets around occasionally. You may need to do this step in batches. Place cooked cutlets on a platter or cutting board.

Discard excess oil in the pan (pour into a heatproof bowl and discard safely). Heat the skillet over medium heat and add the wine, using a wooden spatula to scrape up any bits stuck in the pan. Simmer until reduced by half, about 1 to 2 minutes. Stir in the chicken broth and simmer until reduced in half, and slightly thickened, about 10 minutes. Add a pinch of salt and pepper to the sauce. Taste and add more salt, if desired.

Stir in the chilled butter until melted. Place the chicken cutlets in the sauce and simmer until heated through, only 3 to 5 minutes. Remove the toothpicks and then serve at once passing extra sauce on the side.