Prepare the Grill:

Preheat your grill to a consistent temperature of 375°F to ensure even cooking.

Stuff the Chicken:

Using a sharp knife, carefully cut a pocket into each chicken breast. Lay a slice of Swiss cheese on top of a slice of deli ham and roll them together tightly. Insert the rolled ham and cheese into the pocket of each chicken breast, securing the opening with toothpicks to prevent spillage during grilling.

Season the Chicken:

Generously coat both sides of each stuffed chicken breast with the chicken seasoning, ensuring an even application to enhance the flavor.

Grill the Chicken:

Place the prepared chicken directly onto the grill grates. Cook for approximately 15 to 18 minutes on each side, flipping once. The chicken is done when its internal temperature reaches 165°F.

Prepare the Dijon Sauce:

In a small mixing bowl, combine mayonnaise, Dijon mustard, apple cider vinegar, brown sugar, cayenne pepper, salt, and black pepper. Mix thoroughly until the sauce is smooth and well-blended. Chill the sauce until it is ready to be served.

Rest and Serve:

Remove the chicken from the grill and allow it to rest for 10 minutes. Serve the grilled chicken cordon bleu with the chilled Dijon cream sauce on the side for dipping or drizzling.