Pre-heat the oven to 400º. Take each chicken breast and make a pocket by carefully cutting a slit on the sides of the chicken with a sharp knife without cutting through the chicken.
Gently open up the chicken breasts.
Place 2 slices of Swiss cheese, 2 slices of ham and a tablespoon of the dill pickle inside each chicken breast and spread it out to create a thin layer. Roll up your chicken and secure with a toothpick.
To a shallow bowl, add the flour and add in a dash of salt and pepper. Dip each chicken roll in flour, and then in the egg wash, and finally roll them in breadcrumbs until fully coated. Be sure to shake off any excess flour and egg wash before rolling it in breadcrumbs for a more even coating.
Arrange the chicken on the baking sheet and bake the chicken for 25-30 minutes or until the chicken reaches an internal temperature of 165 degrees F and the breadcrumbs are golden brown.
While the chicken is baking, melt butter in a saucepan over medium heat. Add in the flour and whisk til incorporated. Whisk in heavy cream and cook for about 1 minute. Add Dijon mustard, dill and Parmesan cheese. Simmer the sauce for 2-3 minutes until it thickens.
Remove the toothpicks from the chicken and drizzle with the creamy sauce. Enjoy!