Place each chicken breast between two sheets of plastic wrap and gently pound with a meat mallet until about 1/2 inch thick for even cooking.

Season both sides of each flattened chicken breast generously with salt and pepper. Lay 2 prosciutto slices on top of each breast, overlapping slightly to cover completely, then place 1 sage leaf in the center. Press gently so everything adheres together.

Spread flour on a shallow plate. Lightly dredge only the prosciutto side of each chicken breast in flour, shaking off excess.

Heat olive oil and 2 tablespoons butter in a large 12-inch skillet over medium-high heat until butter stops foaming, about 2 minutes.

Place chicken breasts in pan, prosciutto side down. Cook without moving for 4-5 minutes until prosciutto turns golden and crispy.

Flip chicken, add remaining 2 tablespoons butter to pan, and cook for another 4-5 minutes until internal temperature reaches 165°F. Transfer chicken to a warm plate and tent loosely with aluminum foil.

Pour chicken broth and white wine into the same skillet, scraping up browned bits from bottom. Bring to a simmer and cook for 2-3 minutes until sauce thickens slightly.

Return chicken to pan, spoon sauce over top, and let warm through for 1 minute before serving immediately.