Preheat your oven to 350°F (175°C) and flatten the chicken breasts to about ¼-inch thickness using a meat mallet. Season each piece generously with salt and pepper.

Lay two slices of Swiss cheese and a few slices of ham on each flattened chicken breast.

Carefully roll each chicken breast up, starting from the edge where the filling is placed, and secure with toothpicks.

Dredge each rolled chicken piece in flour, then dip in beaten eggs, and coat with panko breadcrumbs.

In a skillet, melt the butter and olive oil together, then sear the chicken rolls for about 5 minutes until golden brown.

Transfer the chicken rolls to a baking dish and bake for 20-25 minutes until the chicken reaches an internal temperature of 165°F (75°C).

In a saucepan, melt 2 tablespoons of butter, whisk in the flour to create a roux, then gradually add milk while whisking continuously.

Continue to whisk the sauce until it thickens, then stir in Parmesan cheese and Dijon mustard.

Once the chicken is done, remove the toothpicks and drizzle the creamy sauce over the chicken rolls.