Season chicken with salt and pepper, to taste. Place the flour in a shallow dish. Lightly dredge the chicken with flour on both sides, shaking off the excess.
In a small bowl combine the chicken broth, lemon juice, Dijon mustard and 1 teaspoon of the reserved flour, whisk until smooth. Heat a large nonstick skillet over medium-high heat. Melt the butter and add 1 teaspoon of the olive oil and half of the chicken. Cook 2 minutes on each side, until slightly golden, then transfer to a dish. Add remaining ½ teaspoon olive oil and remaining chicken and cook 2 minutes on each side. Set aside on a dish with the other pieces of chicken.
Reduce the heat to medium-low, add the chicken broth mixture. Whisk scraping up any bits stuck to the pan then simmer 2 minutes to reduce slightly. Return the chicken to the skillet, top each piece with a slice of ham and a slice of cheese, cover the skillet and simmer medium-low for 3 to 4 minutes until the cheese melts.
To serve use a spatula and transfer the chicken to each dish, spoon the remaining sauce over each piece. Sprinkle with the parsley and toasted panko (bread) crumbs.
