Preheat your oven to 350°F (175°C).

Pound the chicken breasts down to about 1/4-inch thickness and season with salt and pepper.

Layer 2 slices of Swiss cheese and 2 slices of ham on each chicken breast.

Roll each breast tightly from the narrow end and secure with toothpicks.

Set up your dredging station: arrange plates with flour, beaten eggs, and panko breadcrumbs.

Dredge each roll first in flour, then coat it in the egg, and finally press into the breadcrumbs.

Heat a skillet over medium heat with butter and olive oil. Brown the chicken rolls on all sides for about 5 minutes.

Transfer the chicken rolls to a baking dish and bake for 20–25 minutes.

Meanwhile, prepare the cream sauce: melt butter, add flour to create a roux, and whisk until bubbly.

Gradually whisk in the milk and stir in the Parmesan cheese and Dijon mustard.

Serve the chicken rolls warm, topped with the cream sauce and remove toothpicks.