1Place each chicken breast between two pieces of parchment paper and pound to 1/4-inch thickness.
2Season both sides of the pounded chicken with salt and black pepper.
3Layer 2 slices of ham and 2 slices of Swiss cheese on each chicken breast.
4Roll up the chicken tightly, stuffing the cheese and meat in as you go.
5Repeat this process for 4 total chicken breasts.
6Preheat your oven to 450 degrees Fahrenheit if baking.
7Heat 1/2 cup of vegetable oil in a large skillet to 350 degrees Fahrenheit if frying.
8Prepare a dipping station with three bowls: the first with 1/2 cup of all-purpose flour, the second with 1 large egg whisked with 1 tablespoon of water, and the third with 1 cup of plain bread crumbs.
9Roll each stuffed chicken breast in flour to coat.
10Then roll the chicken in the egg mixture.
11Finally, roll the chicken in the breadcrumbs to finish coating.
12For the baked version, lightly grease a 9x13 pan (or smaller if making fewer portions) and place the chicken seam side down into the pan.
13Bake in the 450-degree oven for 25-30 minutes, until the internal temperature reaches 165 degrees Fahrenheit.
14For the fried version, place the breaded chicken seam side down directly into the 350-degree oil.
15Cook the fried chicken for 4-5 minutes per side until golden brown.
16To make the dijon sauce, melt 2 tablespoons of salted butter in a small saucepan over medium heat.
17Whisk in 1 tablespoon of cornstarch until all white specs are gone.
18Pour in 1 teaspoon of apple cider vinegar, 1 tablespoon of brown sugar, and 1 tablespoon of dijon mustard.
19Slowly whisk in 1 cup of milk and bring the mixture to a simmer.
20After 2 or 3 minutes, the sauce will start to simmer and thicken up.
21Pour the finished sauce into a small serving dish.
22Once the chicken reaches an internal temperature of 165 degrees Fahrenheit, it is ready to eat.
23Serve the chicken whole or sliced, immediately, and drizzle with the delicious sauce.