Step 1: Prepare the Chicken : Place each chicken breast between two sheets of plastic wrap. Using a meat mallet or rolling pin, gently pound until ¼-inch thick. Season lightly with salt and black pepper (go easy on the salt — prosciutto is salty).
Step 2: Assemble the Saltimbocca : Place one or two sage leaves on each piece of chicken. Lay a slice of prosciutto over the top, pressing gently so it adheres. Lightly dredge the underside (the chicken side) in flour, shaking off excess.
Step 3: Sear the Chicken :Heat olive oil and 2 tablespoons of butter in a large skillet over medium-high heat. Place the chicken in the pan, prosciutto side down first. Cook for 2–3 minutes until the prosciutto becomes crisp, then flip and cook another 2–3 minutes on the other side until golden and cooked through. Transfer to a plate and keep warm.
Step 4: Make the Pan Sauce : In the same pan, add white wine and scrape up any browned bits from the bottom. Let the wine reduce by half, about 2–3 minutes. Add chicken broth and lemon juice, simmering for another 3–4 minutes until slightly thickened. Turn off heat and whisk in 2 tablespoons butter until the sauce is glossy.
Step 5: Combine and Serve : Return the chicken to the skillet and spoon sauce over each piece. Let it sit for 1–2 minutes to soak up the flavors before serving.