Prepare the Parmesan Dijon Sauce: In a medium saucepan over low heat, melt 2 tablespoons of butter. Whisk in 2 tablespoons of flour until bubbly, then gradually add 1 cup of milk and 1 chicken bouillon cube. Stir constantly for about 5 minutes until thickened. Mix in 2 tablespoons of Dijon mustard and ½ cup of grated Parmesan cheese until smooth.

Assemble Quesadillas: Lay out a flour tortilla, spread a layer of the sauce, then layer ½ cup of shredded Swiss cheese, deli ham slices, grilled chicken, and toasted breadcrumbs. Top with another ½ cup of cheese. Fold the tortilla in half.

Cook Quesadilla: In a skillet over medium heat, melt 1 tablespoon of butter. Place the quesadilla in the skillet and cook for 3-4 minutes until golden. Flip and cook the other side for an additional 3-4 minutes until both sides are golden and cheese is melted.

Serve with Sauce: Transfer cooked quesadilla to a board, let it rest for a minute, cut into triangles, and serve warm with remaining sauce.