Prepare the Chicken:
Pound the chicken breasts to about ¼-inch thickness. Season lightly with salt and pepper.
Place 1–2 sage leaves on each chicken piece and top with a slice of prosciutto. Use toothpicks to secure the prosciutto and sage to the chicken.
Dredge the Chicken:
Lightly coat both sides of the chicken in flour, shaking off any excess.
Sear the Chicken:
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Add the chicken, prosciutto-side down, and cook for 3–4 minutes per side until golden brown and cooked through. Transfer to a plate and cover to keep warm.
Make the Sauce:
Reduce the heat to medium and add the white wine to the skillet. Scrape up any browned bits from the bottom.
Stir in the chicken broth and simmer for 3–4 minutes until slightly reduced. Swirl in the remaining butter for a rich finish.
Combine and Serve:
Return the chicken to the skillet, spooning the sauce over the top to coat. Simmer for 1–2 minutes to meld the flavors.
Remove toothpicks, garnish with extra sage if desired, and serve with lemon wedges.