Pound the chicken breasts between two sheets of plastic wrap until they are about 1/4 inch thick.
Place a slice of ham and cheese on each piece of chicken. Roll up and secure with toothpicks.
In a shallow bowl, whisk together the eggs and Dijon mustard.
In another shallow bowl, mix together the flour, salt, and pepper.
In a third shallow bowl, mix together the panko breadcrumbs and Parmesan cheese.
Dip each chicken roll in the flour mixture, then the egg mixture, and finally coat with the breadcrumb mixture.
Heat olive oil in an oven safe skillet over medium heat. Brown each side of the chicken rolls for about 5 minutes.
Transfer the skillet to the oven and bake for 25 minutes or until the chicken is cooked.
While the chicken bakes, melt butter in a saucepan over medium heat. Whisk in flour and cook for 1 minute. Slowly pour in chicken broth, stirring constantly until smooth. Add cream and let simmer until thickened.
Once the chicken is done baking, remove it from the oven and let cool for a few minutes before removing toothpicks.
Serve with the creamy sauce on top of the chicken rolls.
Notes
For the best results, use a thermometer to ensure the chicken is fully cooked before serving.
Use gluten-free panko breadcrumbs to make a gluten-free variation.
For the finest flavor, use deli style ham.
To make it hotter, add a little bit of cayenne pepper to the breadcrumb mixture.
To create the mustard sauce, go to step 5 and refrigerate for up to 3 days. Reheat the sauce in a saucepan over medium heat when ready to serve.
If you want to improve the meal's flavor, add a sprinkle of fresh thyme or rosemary to the breadcrumb mixture.