Season both sides of the chicken cutlets with salt and pepper.
Sprinkle 1/2 teaspoon minced sage on one side of each cutlet, top with a slice of prosciutto, and press to adhere. Place a sage leaf on each and secure with a toothpick.
Heat olive oil in a skillet over medium heat. Cook cutlets, prosciutto side down, for about 3 minutes. Flip and continue cooking until done, about 3-5 more minutes. Remove and cover with foil.
Discard half the skillet oil, leaving about 1 teaspoon. Sauté shallot for 2 minutes, then add flour and cook for 1 minute.
Whisk in wine and broth, scraping up any browned bits. Simmer until sauce thickens slightly, about 4 minutes.
Reduce heat to low, whisk in butter, parsley, and lemon juice. Return chicken to skillet, heat through for about 1 minute.
Serve chicken with sauce evenly divided among the cutlets.