Preheat oven to 350 degrees F.

Prepare breadcrumb mixture by combining breadcrumbs, parmesan, herbs, and melted butter. Set into a shallow dish and set aside.

Prepare egg and flour needed for dredging by putting each in a separate shallow dish. Set aside.

To prepare chicken, flatten to a uniform thickness of 1/4 inch by smashing with a meat tenderizer or rolling pin in between two sheets of plastic wrap. For each breast, set 2 pieces of swiss cheese wrapped in two pieces of ham in the center of each flattened breast. Wrap the chicken around the ham and swiss and use toothpicks to secure.

To bake, dip each stuffed breast in flour, then egg,  then press both sides firmly into the breadcrumb mixture to fully coat.

Set on parchment lined baking sheet and bake in preheated oven for 25-30 minutes.

While the chicken is baking, make the dijon sauce. In a small saucepan over medium heat, melt the butter. Add the flour to the melted butter, whisk, and allow to cook for several minutes while continually whisking to avoid burning. Once the flour has started to cook, whisk in milk. Continue to heat until the milk bubbles and begins to thicken, about 3-5 minutes. Remove from heat and whisk in dijon, parmesan, and thyme. Add salt and pepper to taste.