In a medium saucepan over low heat, melt 4 tablespoons of butter until bubbly. Whisk in 3 tablespoons of flour to form a roux, cooking for about 2 minutes until it turns a light golden color. Gradually add 1 cup of milk while whisking to prevent lumps, then stir in 1 chicken bouillon cube, 2 tablespoons of Dijon mustard, and ½ cup of grated Parmesan cheese. Keep the sauce warm while you prepare the quesadillas.

Heat a large skillet over medium heat and add 1 tablespoon of melted butter. Take one tortilla and layer it with ½ cup of Swiss cheese, 2 ounces of deli ham, 1 cup of shredded grilled chicken, and a generous drizzle of your creamy Parmesan sauce. Sprinkle 2 tablespoons of toasted breadcrumbs and top with another ½ cup of cheese before placing a second tortilla on top.

Carefully transfer the quesadilla into the hot skillet, cooking for 3-4 minutes until the bottom is golden brown and the cheese starts to melt. With a spatula, gently flip the quesadilla and add another tablespoon of melted butter if needed. Cook the second side for another 3-4 minutes.

Once both sides are golden brown and crispy, transfer your Chicken Cordon Bleu Quesadilla to a cutting board. Allow it to cool for a minute before cutting into wedges with a sharp knife. Serve warm with any remaining creamy Parmesan Dijon sauce drizzled on the side.