Season both sides of the chicken cutlets with salt.

Working one at a time, top each cutlet with a slice of prosciutto, applying pressure to create a strong bond. Wrap the excess prosciutto around the cutlet and press it into place on the underside.

Place two sage leaves decoratively onto each cutlet, securing them in place with toothpicks.

Coat both sides of the cutlets with the flour, shaking off any excess, and transfer to a plate; reserve 1 tablespoon of the flour.

Heat a large skillet over medium heat.

Add 2 tablespoons of the olive oil to the pan and cook the chicken, in batches, adding more oil as needed, until the prosciutto is crispy and the chicken is cooked through, for 2½ to 3 minutes per side; transfer to a serving platter.

Add the wine, increase the heat to high, bring to a simmer and cook until slightly reduced, scraping the bottom of the pan to remove any fond, for 1 to 2 minutes.

Add the chicken broth and return to a simmer.

Meanwhile, combine the butter and reserved flour mixture to form a paste.

Add the butter mixture and whisk to combine.

Cook, whisking constantly until slightly thickened, for 2 minutes.

Season with salt and pepper, to taste.

Pour the sauce over the chicken and serve immediately. Remove the toothpicks before serving.