Pound chicken breasts to 1/4-inch thickness and season with salt, pepper, garlic powder, and paprika.
Lay out each piece, place a slice of ham and cheese on top, and roll tightly, securing with toothpicks.
Freeze the rolls for 10-15 minutes to help them hold their shape.
Coat each roll in flour, dip into beaten eggs, and coat with panko breadcrumbs.
For frying: Heat oil in a pan and fry for 3-4 minutes per side until golden brown.
For baking: Preheat oven to 375°F (190°C), place chicken on a lined baking sheet, and bake for 25-30 minutes.
For air-frying: Cook at 375°F (190°C) for 12-15 minutes, flipping halfway.
To make the sauce: Melt butter in a saucepan, whisk in flour, then gradually add milk, Dijon mustard, and nutmeg. Stir until thickened.
Let the chicken rest for 5 minutes, slice, drizzle with sauce, and serve with your favorite sides.