Dredge the chicken: In a medium shallow bowl, add the flour and season with a pinch of salt and a few grinds of black pepper. In a second medium shallow bowl, add the eggs, mustard, paprika, a pinch of salt and a few grinds of pepper; whisk to combine. In the third medium shallow bowl, add the panko. Run each piece of chicken through these bowls in the order of setting them up, so flour, egg then panko.
Fry the chicken: In a straight-sided large pan, add enough oil to just cover the bottom by about a quarter inch. Heat on medium-high and when oil begins to swirl, add the chicken in batches, placing each piece in the oil away from you so there is less splatter. Add more oil between batches if needed. Remove each piece of chicken to a baking sheet.
Finish the chicken: Turn on the broiler or heat the oven to the highest temperature possible. Top each piece of chicken with 2 slices of ham and 1 slice of cheese. Place in the oven and cook until the cheese is melted, about 2-3 minutes. Remove and serve.
Party Tip: Turn these into small bites for guests by cutting the chicken into bite-sized cubes before cooking then topping with cut squares of ham and cheese. Insert a toothpick in each and enjoy a fun cocktail party bite