Place each piece of chicken between two sheets of plastic wrap, then pound them until they are ½-inch thick all around. (Try not to make any holes while doing this.)
Season both sides of the chicken with a generous amount of salt and black pepper, then layer 2-3 pieces of ham on the lower half and layer on 2-3 slices of cheese on top of the ham.
Tightly roll up the chicken and use some plastic wrap to wrap around the chicken, then tightly twist the ends so that the ham and cheese are completely covered by the chicken.
Chill in the refrigerator for at least 45 minutes or up to 4 hours.
Preheat the oven to 350 degrees and grease a large baking sheet or baking dish with cooking spray. Set aside.
Whisk the flour, salt, pepper, onion powder, garlic powder, and paprika together in a shallow bowl, then whisk the eggs and chicken broth together in a shallow bowl, and finally, pour the breadcrumbs into a separate shallow bowl.
Roll each of the chicken rolls one at a time in the flour, dusting off the excess flour, then cover in the egg mixture, drain, and roll in the breadcrumbs until fully coated.
Place the chicken on the baking sheet, evenly spaced, and bake for 25 minutes. Increase the heat to 425℉ and bake for another 5-10 minutes or until the breadcrumbs start to turn a golden brown and the chicken reaches 165 degrees Fahrenheit.
While the chicken is baking, melt the butter in a medium saucepan over medium heat and add the flour. Whisk until the flour turns light golden, then whisk in the mustard and honey. Slowly add the milk, whisking the entire time, and let it simmer until it starts to thicken, about 5 minutes.
Remove the pan from the heat and serve the chicken with the rich and creamy honey dijon sauce. Garnish with a bit of fresh parsley if desired.