Season the chicken breasts evenly with salt, pepper, garlic powder, and onion powder.

Place each chicken breast between plastic wrap and pound to about ½ inch thick.

Layer 2 slices Swiss cheese, 2 slices ham, another layer of Swiss, and another layer of ham onto each pounded chicken breast, then roll it up.

Tightly wrap the rolled chicken in plastic wrap, twisting the ends to firm the roll, then chill in the fridge for 30 minutes to set.

Meanwhile, preheat 2 inches of oil in a tall-sided pan to 325°F (170°C).

After chilling, dredge each chicken roll through flour, then beaten egg, and finally panko bread crumbs.

Fry the breaded chicken in the preheated oil for about 5 minutes per side until golden brown; if needed, finish cooking on a wire rack in a 325°F (170°C) oven until an internal temperature of 165°F (75°C) is reached.

Concurrently, melt butter in a 1 ½-quart saucepan over medium heat and cook minced garlic until soft, then whisk in 3 tablespoons of flour for 1 minute.

Gradually whisk in 2 cups of milk until fully combined with the roux, ensuring no lumps remain, and continue whisking until the mixture simmers and thickens.

Stir in the Dijon mustard, Parmesan cheese, salt, and pepper, then remove the pan from the heat.

Slice the cooked chicken cordon bleu and serve immediately, drizzled generously with the prepared Dijon sauce.