In a medium saucepan, melt 2 tablespoons of butter over medium heat. Whisk in 1 tablespoon of all-purpose flour and cook for 1-2 minutes until golden. Gradually add 1 cup of milk while whisking continuously to avoid lumps. Stir in a chicken bouillon cube, 1 tablespoon of Dijon mustard, and a dash of hot sauce if desired. Cook for about 5 minutes until the sauce thickens, then mix in ½ cup of freshly grated Parmesan cheese and keep warm.

In a skillet, heat 2 tablespoons of melted butter over medium heat. Place a flour tortilla in the pan and evenly layer half of the Swiss or provolone cheese slices, followed by the sliced grilled chicken and deli ham. Sprinkle the toasted breadcrumbs for added crunch, then pour a little of the prepared Parmesan Dijon sauce over the top, finishing with the remaining cheese. Top with another tortilla.

Cook the quesadilla for about 3-4 minutes or until the bottom tortilla is golden brown. Carefully flip the quesadilla using a large spatula and cook for another 3-4 minutes on the other side, until crispy and cheese is melted.

Once cooked, transfer the quesadilla to a cutting board, let it cool for a minute, and slice into wedges. Serve warm with remaining Parmesan Dijon sauce on the side.