Preheat the oven to 350° F. Line a baking sheet with parchment or a silicone mat and lightly grease it with nonstick spray; set aside.
For Roulade
Trim the fat from the chicken breasts and butterfly them lengthwise. Place each chicken breast between two sheets of plastic wrap on a large cutting board.
Using a meat tenderizer mallet, beat the chicken breast until about ¼ inch thick. Repeat with remaining chicken breasts.
Brush or spread a thin layer of dijon mustard over each flattened chicken breast.
Sprinkle the salt and pepper over each of the chicken breasts.
Place a single thin layer of ham then a layer of prosiutto followed by a layer of swiss cheese and a final layer of gruyere (you may not need to use all of the hams or cheeses).
Roll up each of the chicken breasts like a burrito. To do this, first fold in the short ends slightly then roll up from one long edge to the other. Secure with toothpicks if necessary. You now have a roulade.
For Crust
In a shallow dish, whisk together the egg and hot sauce.
In a second shallow dish, mix together the remaining crust ingredients.
Roll each roulade in the egg mixture then in the crust mixture. Place on the prepared sheet pan.
Bake for 30 to 45 minutes or until the internal temperature reads 165° F.
Remove from the oven and allow to rest at room temperature for about 10 minutes.
For Sauce
Meanwhile, mix together all of the sauce ingredients except the gluccie in a medium saucepan over medium-high heat until butter and cheese have melted. Remove from the heat.
If you would like the sauce to be thicker, sprinkle then whisk in the gluccie.
To Serve
Once the chicken has rested for 10 minutes, use a sharp knife to slice it into 1 inch thick slices.