Preheat the Smoker: Begin by setting your smoker to a temperature of 275°F. Allow it to fully preheat before proceeding with the recipe.

Prepare the Chicken: Create a pocket in each chicken breast using the tip of a sharp knife. On a flat surface, lay out the ham slices, placing one slice of Swiss cheese atop each piece. Roll the ham and cheese together, using two ham slices per piece of cheese. Insert the rolled ham and cheese into the pocket of each chicken breast, securing the opening with toothpicks to prevent any filling from escaping during cooking.

Coat the Chicken: In one shallow dish, lightly whisk the eggs and milk to create the wet dredge. In a separate dish, combine the panko breadcrumbs with the chicken seasoning to form the dry dredge. Dip each stuffed chicken breast into the egg mixture, ensuring it is thoroughly coated, and then press it into the seasoned breadcrumbs until evenly covered on all sides.

Smoke the Chicken: Position the prepared chicken breasts directly onto the grates of the preheated smoker. Close the lid and smoke for approximately 60 to 90 minutes, flipping each piece once midway through. Remove the chicken from the smoker once its internal temperature reaches 165°F, as measured by a meat thermometer.

Prepare the Dijon Cream Sauce: In a small bowl, combine mayonnaise, Dijon mustard, apple cider vinegar, brown sugar, cayenne pepper, salt, and black pepper. Mix thoroughly until the ingredients are well blended. Keep the sauce chilled until ready to serve.

Rest and Serve: Remove the smoked chicken cordon bleu from the smoker and allow it to rest for 10 minutes. Serve warm, accompanied by the prepared Dijon cream sauce for a flavorful finish.