Pound chicken into 4 thin pieces. Season chicken with salt and pepper, to taste. Place flour in a shallow dish. Lightly dredge chicken with flour on both sides.
In a small bowl, combine chicken broth, lemon juice, and Dijon mustard.
Coat a large, nonstick pan with cooking spray. Add butter and heat to melt over medium-high heat. Add chicken breasts and cook 2 minutes on each side, until slightly golden, then transfer to a dish. Note: If your pan isn’t large enough to cook all 4 pieces of chicken, cook in batches. Heat only ¾ tablespoon butter to cook each batch. Set cooked chicken aside on a plate.
Reduce heat to medium-low, add chicken broth mixture. Mix around, using a rubber spatula, scraping up any bits stuck to pan. Simmer for 2-3 minutes to reduce sauce slightly. Return chicken to pan. Top each piece with 1 slice of ham and 1 slice of cheese. Cover pan and simmer over medium-low heat for 3 to 4 minutes, until the cheese is melted.
To serve: Use a spatula to transfer chicken to each plate. Spoon remaining sauce over each piece of chicken.