Preheat the oven to 350°F (175°C).
Pound chicken breasts to about 1/4-inch thickness and season with salt and pepper.
Place 2 slices of Swiss cheese and 2 slices of ham on each chicken breast.
Roll up the chicken breasts carefully and secure with toothpicks.
Dredge each chicken roll in flour, dip in beaten eggs, then coat with panko breadcrumbs.
Heat butter and olive oil in a large skillet over medium heat and brown the chicken rolls on all sides until golden, about 5 minutes.
Transfer browned chicken rolls to a baking dish and bake for 20-25 minutes until cooked through.
To make the cream sauce, melt butter in a saucepan over medium heat and whisk in flour, cooking for 1 minute until smooth.
Slowly add milk while whisking continuously until the sauce thickens.
Stir in Parmesan cheese and Dijon mustard, season with salt and pepper to taste.
Remove chicken from oven, discard toothpicks, and serve with cream sauce poured over the top.