Split the chicken breasts horizontally into two scallops, then pound them gently to flatten them out a bit more. Trim off any bits of gristle or strands of meat. Season the scallops generously with salt on both sides, then wrap them up and chill for at least 30 minutes, or until you are ready to cook.
Heat olive oil and a knob of butter in a skillet large enough to hold all the scallops in one layer. Meanwhile, lightly flour the chicken scallops and, when the butter melts and is about to turn brown, add lay them in the skillet. Brown the scallops over lively heat until they are lightly browned on both sides.
Add a splash of white wine to the skillet, turning the scallops so they are covered on both sides with the pan juices. Lower the heat, then lay one ham slice on each scallop, followed by a slice of cheese.
Cover the skillet and let the scallops simmer, just until the cheese has melted entirely, no more than a minute or so.
Transfer the scallops to a serving dish and nap them with the cooking juices in the skillet. If you like sprinkle with minced parsley for color, then serve with they're still warm.