Place each chicken breast half between sheets of plastic wrap and pound with a rolling pin to about 1/8-inch thickness, trying to get nearly rectangular shape. Season with salt and pepper to taste.
Arrange 4 slices of cheese on each chicken. Arrange ham slices over cheese. Then arrange another layer of cheese over the ham. Starting from the wider side, roll tightly each chicken breast with ham and cheese inside. Wrap each chicken breast in plastic wrap and twist the ends to tight the roll. Freeze 20-to 30 minutes to slightly firm on the outside.
When ready to fry, heat the oil in a large skillet or deep fryer. Prepare dishes with flour, eggs and breadcrumbs to dip the chicken.
Unwrap the rolls from plastic wrap and dip in flour to cover completely. Next dip in eggs. Finally dip in breadcrumbs.
Fry until breadcrumbs are golden-brown and the chicken is cooked through.
To make the sauce in a saucepan melt the butter. Add garlic powder and flour, stir for 1-2 minutes over medium heat, then whisk in milk. Whisk in mustard and grated Parmesan cheese. Season with salt and pepper to taste. Cook for a few more minutes, whisking constantly, until it thickens.
