Slice chicken breasts in half length wise. Place pieces, one at a time, in a resealable plastic bag, then pound with a meat mallet until 1/4" thick. Season both sides of the breasts with salt and pepper. Saute 2 pieces of chicken in oil in a saute pan over medium-high heat until browned,3-S minutes.Turn and cook 2 more minutes, then transfer to a plate and tent with foil to keep warm. Saute remaining chicken in the same manner. Cook mushrooms in the saute pan over high heat,S minutes, or until beginning to brown. Add additional oil as needed to prevent burning. Deglaze with marsala, scraping up any browned bits, then add broth and bring to a boil. Simmer until liquid is reduced by half,S minutes. Off heat, stir in prosciutto, sage, and butter until butter melts. Season with salt and pepper.