Place chicken breasts in a zipper bag, and pound to even thickness. Cut each piece in half to make 8 pieces.
Combine Parmesan, salt, and pepper in a pie plate. Whisk together with a fork.
Dredge each piece of chicken in the Parmesan mixture, coating all sides.
Combine chicken broth, lemon juice, white wine, and dijon mustard.
In a large skillet, over medium heat, melt the butter with the olive oil. Sauté the chicken pieces for 4 minutes per side. Remove to a plate . Top each piece with a slice of ham and a slice of cheese. Cover for a few minutes until the ham is warm and the cheese has melted. Return chicken to the skillet.
Increase the heat to medium high, and pour the broth/lemon juice mixture into the skillet. Whisking up all the browned bits from the bottom, bring the mixture to a boil. Simmer for several minutes until reduced by half. . Boil for 2 minutes or more if needed.
Serve immediately, sprinkled with fresh parsley and topped with the sauce.