Put chicken breasts between pieces of plastic wrap and, using a rolling pin or the smooth side of a meat mallet, bash them to a thickness of about ¼ inch, but don't bash so hard that they break up. Season with pepper. Wrap a slice of prosciutto around each chicken escalope and put a sage leaf or two on top. Lightly dust the chicken on both sides with flour.
Heat butter and oil in a large skillet over medium heat. Cook the chicken until no longer pink in the middle, about 3 minutes per side. To check if it's done, stick the tip of a sharp knife into it: the juice that runs out should be clear with no trace of pink. Transfer the chicken to a warm platter and cover with foil.
Add Marsala to the pan and cook over high heat until thickened and reduced by about half, 3 to 4 minutes. Serve the sauce over the chicken.
